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Theosophical Book 

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133 r ^ tne P resent ti 1116 our actions are largely in- 
fluenced by our theories. We have aban- 
doned the simple and instinctive mode of life 
of the earlier civilisations for one regulated 
by the assumptions of our knowledge and supplemented 
by all the devices of intelligence. In such a state it is 
possible to conceive that a danger may arise, not only 
from a want of knowledge and practical skill, but even 
from the very presence and possession of them in any one 
department, if there is a lack of information in other 
departments. If, for instance, with our present knowledge 
of physical laws and mechanical skill, we were to build 
houses without regard to the conditions laid down by 
physiology, we should probably to suit an apparent 
convenience make them perfectly draught-tight, and the 
best-constructed mansions would be full of suffocating 
chambers. The knowledge of the construction of the 
body and the conditions of its health prevent it from 
suffering injury by the development of our powers over 

In no dissimilar way the mental balance is saved from 
the dangers attending an attention concentrated on the 

4 What is the Fourth Dimension ? 

Jaws of mechanical science by a just consideration of the 
constitution of the knowing faculty, and the conditions of 
knowledge. Whatever pursuit we are engaged in, we are 
acting consciously or unconsciously upon some theory, 
some view of things. And when the limits of daily 
routine are continually narrowed by the ever-increasing 
complication of our civilisation, it becomes doubly impor- 
tant that not one only but every kind of thought shoi Id 
be shared in. 

There are two ways of passing beyond the domain of 
practical certainty, and of looking into the vast range of 
possibility. One is by asking, " What is knowledge ? 
What constitutes experience ? " If we adopt this course 
we are plunged into a sea of speculation. Were it not 
that the highest faculties of the mind find therein so 
ample a range, we should return to the solid ground of 
facts, with simply a feeling of relief at escaping from so 
great a confusion and contradictoriness. 

The other path which leads us beyond the horizon of 
actual experience is that of questioning whatever seems 
arbitrary and irrationally limited in the domain of know- 
edge. Such a questioning has often been successfully 
applied in the search for new facts. For a long time four 
gases were considered incapable of being reduced to the 
liquid state. It is but lately that a physicist has succeeded 
in showing that there is no such arbitrary distinction among 
gases. Recently again the question has been raised, " Is 
there not a fourth state of matter ? " Solid, liquid, and 
gaseous states are known. Mr. Crookes attempts to 
demonstrate the existence of a state differing from all of 
these. It is the object of these pages to show that, by 
supposing away certain limitations of the fundamental 
conditions of existence as we know it, a state of being 
can be conceived with powers far transcending our own. 
When this is made clear it will not be out of place to 

What is the Fourth Dimension ? 5 

n vestigate what relations would subsist between our 
mode of existence and that which will be seen to be 
a possible one. 

In the first place, what is the limitation that we must 
suppose away ? 

An observer standing in the corner of a room has three 
directions naturally marked out for him ; one is upwards 
along the line of meeting of the two walls ; another is 
forwards where the floor meets one of the walls ; a third 
is sideways where the floor meets the other wall. He 
can proceed to any part of the floor of the room by 
moving first the right distance along one wall, and then 
by turning at right angles and walking parallel to the 
other wall. He walks in this case first of all in the 
direction of one of the straight lines that meet in the 
corner of the floor, afterwards in the direction of the 
other. By going more or less in one direction or the 
other, he can reach any point on the floor, and any move- 
ment, however circuitous, can be resolved into simple 
movements in these two directions. 

But by moving in these two directions he is unable to 
raise himself in the room. If he wished to touch a point 
in the ceiling, he would have to move in the direction of 
the line in which the two walls meet. There are three 
directions then, each at right angles to both the other, 
and entirely independent of one another. By moving 
in these three directions or combinations of them, it is 
possible to arrive at any point in a room. And if we 
suppose the straight lines which meet in the corner of 
the room to be prolonged indefinitely, it would be 
possible by moving in the direction of those three lines, 
to arrive at any point in space. Thus in space there 
are three independent directions, and only three; every 
other direction is compounded of these three. The 
question that comes before us then is this. " Why 

6 What is the Fourth Dimension ? 

should there be three and onty three directions ? " Space, 
as we know it, is subject to a limitation. 

In order to obtain an adequate conception of what 
this limitation is, it is necessary to first imagine beings 
existing in a space more limited than that in which we 
move. Thus we may conceive a being who has been 
throughout all the range of his experience confined to a 
single straight line. Such a being would know what it 
was to move to and fro, but no more. The whole of 
space would be to him but the extension in both direc- 
tions of the straight line to an infinite distance. It is 
evident that two such creatures could never pass one 
another. We can conceive their coming out of the 
straight line and entering it again, but they having 
moved always in one straight line, would have no con- 
ception of any other direction of motion by which such 
a result could be effected. The only shape which could 
exist in a one-dimensional existence of this kind would 
be a finite straight line. There would be no difference in 
the shapes of figures; all that could exist would simply 
be longer or shorter straight lines. 

Again, to go a step higher in the domain of a con- 
ceivable existence. Suppose a being confined to a plane 
superficies, and throughout all the range of its experience 
never to have moved up or down, but simply to have kept 
to this one plane. Suppose, that is, some figure, such 
as a circle or rectangle, to be endowed with the power 
of perception ; such a being if it moves in the plane 
superficies in which it is drawn, will move in a multitude 
of directions ; but, however varied they may seem to be, 
these directions will all be compounded of two, at right 
angles to each other. By no movement so long as the 
plane superficies remains perfectly horizontal, will this 
being move in the direction we call up and down. And 
it is important to notice that the plane would be different, 

What is the Fourth Dimension ? 7 

to a creature confined to it, from what it is to us. We 
think of a plane habitually as having an upper and a 
lower side, because it is only by the contact of solids 
that we realize a plane. But a creature which had been 
confined to a plane during its whole existence would 
have no idea of there being two sides to the plane he 
lived in. In a plane there is simply length and breadth. 
If a creature in it be supposed to know of an up or down 
he must already have gone out of the plane. 

Is it possible, then, that a creature so circumstanced 
would arrive at the notion of there being an up and down, 
a direction different from those to which he had been 
accustomed, and having nothing in common with them ? 
Obviously nothing in the creature's circumstances would 
tell him of it. It could only be by a process of reasoning 
on his part that he could arrive at such a conception. If 
he were to imagine a being confined to a single straight 
line, he might realise that he himself could move in two 
directions, while the creature in a straight line could only 
move in one. Having made this reflection he might ask, 
" But why is the number of directions limited to two ? 
Why should there not be three ? " 

A creature (if such existed), which moves in a plane 
would be much more fortunately circumstanced than one 
which can only move in a straight line. For, in a plane, 
there is a possibility of an infinite variety of shapes, and 
the being we have supposed could come into contact 
with an indefinite number of other beings. He would 
not be limited, as in the case of the creature in a straight 
line, to one only on each side of him. 

It is obvious that it would be possible to play curious 
tricks with a being confined to a plane. If, for instance, 
we suppose such a being to be inside a square, the only 
way out that he could conceive would be through one of 
the sides of the square. If the sides were impenetrable. 

8 What is the Fourtk Dimension ? 

he would be a fast prisoner, and would have no way 

What his case would be we may understand, if we 
reflect what a similar case would be in our own existence. 
The creature is shut in in all the directions he knows of. 
If a man is shut in in all the directions he knows of, he 
must be surrounded by four walls, a roof and a floor. A 
two-dimensional being inside a square would be exactly 
in the same predicament that a man would be, if he were 
in a room with no opening on any side. Now it would 
be possible to us to take up such a being from the inside 
of the square, and to set him down outside it. A being 
to whom this had happened would find himself outside 
the place he had been confined in, and he would not have 
passed through any of the boundaries by which he was 
shut in. The astonishment of such a being can only be 
imagined by comparing it to that which a man would feel, 
if he were suddenly to find himself outside a room in 
which he had been, without having passed through the 
window, doors, chimney or any opening in the walls, 
ceiling or floor. 

Another curious thing that could be effected with a 
two-dimensional being, is the following. Conceive two 
beings at a great distance from one another on a plane 
surface. If the plane surface is bent so that they are 
brought close to one another, they would have no con- 
ception of their proximity, because to each the only possible 
movements would seem to be movements in the surface. 
The two beings might be conceived as so placed, by a 
proper bending of the plane, that they should be absolutely 
in juxtaposition, and yet to all the reasoning faculties of 
either of them a great distance could be proved to inter- 
vene. The bending might be carried so far as to make one 
being suddenly appear in the plane by the side of the other. 
If these beings were ignorant of the existence of a third 

What is the Fourth Dimension ? g 

dimension, this result would be as marvellous to them, as 
it would be for a human being who was at a great 
distance it might be at the other side of the world 
to suddenly appear and really be by our side, and 
during the whole time he not to have left the place in 
which he was. 


THE foregoing examples make it clear that beings can 
be conceived as living in a more limited space than ours. 
Is there a similar limitation in the space we know ? 

At the very threshold of arithmetic an indication of 
such a limitation meets us. 

If there is a straight line before us two inches long, 
its length is expressed by the number 2. Suppose 
a square to be described on the line, the number 
of square inches in this figure is expressed by the 
number 4, i.e., 2x2. This 2 x 2 is generally written 2 2 , 
and named " 2 square." 

Now, of course, the arithmetical process of multiplica- 
tion is in no sense identical with that process by which 
a square is generated from the motion of a straight line, 
or a cube from the motion of a square. But it has 
been observed that the units resulting in each case, 
though different in kind, are the same in number. 

If we touch two things twice over, the act of touching 
has been performed four times. Arithmetically, 2x2 = 4. 
If a square is generated by the motion of a line two inches 
in length, this square contains four square inches. 

So it has come to pass that the second and third powers 
of numbers are called " square " and " cube." 

We have now a straight line two inches long. On 
this a square has been constructed containing four 

io What is the Fourth Dimension ? 

square inches. If on the same line a cube be constructed, 
the number of cubic inches in the figure so made is 8, 
t.e., 2 x 2 x 2 or 2 3 . Here, corresponding to the numbers 
2, 2 2 , 2 s , we have a series of figures. Each figure con- 
tains more units than the last, and in each the unit is of 
a different kind. In the first figure a straight line is the 
unit, viz., one linear inch ; it is said to be of one 
dimension. In the second a square is the unit, viz., one 
square inch. The square is a figure of two dimensions. 
In the third case a cube is the unit, and the cube is of 
three dimensions. The straight line is said to be of one 
dimension because it can be measured only in one way. 
Its length can be taken, but it has no breadth or thick- 
ness. The square is said to be of two dimensions because 
it has both length and breadth. The cube is said to have 
three dimensions, because it can be measured in three 

The question naturally occurs, looking at these num- 
bers 2, 2 2 , 2 3 , by what figure shall we represent 2 4 , or 
2x2x2x2. We know that in the figure there must be 
sixteen units, or twice as many units as in the cube. But 
the unit also itself must be different. And it must not 
differ from a cube simply in shape. It must differ from 
a cube as a cube differs from a square. No number of 
squares will make up a cube, because each square has no 
thickness. In the same way, no number of cubes must 
be able to make up this new unit. And here, instead of 
trying to find something already known, to which the 
idea of a figure corresponding to the fourth power can be 
affixed, let us simply reason out what the properties of 
such a figure must be. In this attempt we have to rely, 
not on a process of touching or vision, such as informs us 
of the properties of bodies in the space we know, but on a 
process of thought. Each fact concerning this unknown 
figure has to be reasoned out ; and it is only after a number 

What is the Fourth Dimension ? 


of steps have been gone through, that any consistent 
familiarity with its properties is obtained. Of all applica- 
tions of the reason, this exploration is perhaps the one 
which requires, for the simplicity of the data involved, the 
greatest exercise of the abstract imagination, and on this 
account is well worth patient attention. The first steps 
are very simple. We must imagine a finite straight line 
to generate a square by moving on the plane of the paper, 
and this square in its turn to generate a cube by moving 
vertically upwards. Fig. I represents a straight line; 
Fig. 2 represents a square formed by the motion of that 
straight line ; Fig. 3 represents perspectively a cube 

formed by the motion of that square A B C D upwards. 
It would be well, instead of using figure 3, to place a cube 
on the paper. Its base would be A B C D, its upper 
surface E F G H. 

The straight line A B gives rise to the square A B C D 
by a movement at right angles to itself. If motion be 
confined to the straight line A B, a backward and forward 
motion is the only one possible. No sideway motion is 
admissible. And if we suppose a being to exist which 
could only move in the straight line A B, it would have 
no idea of any other movement than to and fro. The 
square A B C D is formed from the straight line by a 
movement in a direction entirely different from the direc- 

1 2 What is the Fourth Dimension ? 

tion which exists in A B. This motion is not expressible 
by means of any possible motion in A B. A being which 
existed in A B, and whose experience was limited to what 
could occur in A B, would not be able to understand the 
instructions we should give to make A B trace out the 
figure A B C D. 

In the figure A B C D there is a possibility of moving 
in a variety of directions, so long as all these directions 
are confined to one plane. All directions in this plane 
can be considered as compounded of two, from A to B, 
and from A to C. Out of the infinite variety of such 
directions there is none which tends in a direction perpen- 
dicular to Fig. 2 ; there is none which tends upwards 
from the plane of the paper. Conceive a being to exist 
in the plane, and to move only in it. In all the move- 
ments which he went through there would be none by 
which he could conceive the alteration of Fig. 2 into what 
Fig. 3 represents in perspective. For 2 to become 3 it 
must be supposed to move perpendicularly to its own 
plane. The figure it traces out is the cube ABCDEFGH. 
All the directions, manifold as they are, in which a 
creature existing in Fig. 3 could move, are compounded 
of three directions. From A to B, from A to C, from A 
to E, and there are no other directions known to it. 

But if we suppose something similar to be done to 
Fig. 3, something of the same kind as was done to Fig. I 
to turn it into Fig. 2, or to Fig. 2 to turn it into Fig. 3, 
we must suppose the whole figure as it exists to be moved 
in some direction entirely different from any direction 
within it, and not made up of any combination of the 
directions in it. What is this ? It is the fourth direction. 
We are as unable to imagine it as a creature living in 
the plane Fig. 2 would be to imagine a direction such 
that moving in it the square 2 would become the cube 3. 
The third dimension to such a creature would be as mi- 

What is the Fourth Dimension ? 13 

intelligible as the fourth is to us. And at this point we 
have to give up the aid that is to be got from any present- 
able object, and we have simply to investigate what the 
properties of the simplest figure in four dimensions are, 
by pursuing further the analogy which we know to exist 
between the process of formation of 2 from I, and of 3 
from 2, and finally of 4 from 3. For the sake of conveni- 
ence, let us call the figure we are investigating the 
simplest figure in four dimensions a four-square. 

First of all we must notice, that if a cube be formed 
from a square by the movement of the square in a new 
direction, each point of the interior of the square traces 
out part of the cube. It is not only the bounding lines 
that by their motion form the cube, but each portion of 
the interior of the square generates a portion of the cube. 
So if a cube were to move in the fourth dimension so as 
to generate a four-square, every point in the interior of 
the cube would start de novo, and trace out a portion of 
the new figure uninterfered with by the other points. 

Or, to look at the matter in another light, a being in 
three dimensions, looking down on a square, sees each 
part of it extended before him, and can touch each part 
without having to pass through the surrounding parts, 
for he can go from above, while the surrounding parts 
surround the part he touches only in one plane. 

So a being in four dimensions could look at and touch 
every point of a solid figure. No one part would hide 
another, for he would look at each part from a direction 
which is perfectly different from any in which it is possible 
to pass from one part of the body to another. To pass 
from one part of the body to another it is necessary to 
move in three directions, but a creature in four dimensions 
would look at the solid from a direction which is none of 
these three. 

Let us obtain a few facts about the fourth figure, 

14 What is the Fourth Dimension ? 

proceeding according to the analogy that exists between 
i, 2, 3, and 4. In the Fig. I there are two points. In 2 
there are four points the four corners of the square. In 
3 there are eight points. In the next figure, proceeding 
according to the same law, there would be sixteen points. 

In the Fig. I there is one line. In the square there 
are four lines. In the cube there are twelve lines. How 
many lines would there be in the four-square ? That is 
to say that there are three numbers I, 4, and 12. What 
is the fourth, going on accordingly to the same law ? 

To answer this question let us trace out in more detail 
how the figures change into one another. The line, to 
become the square, moves ; it occupies first of all its 
original position, and last of all its final position. It 
starts as A B, and ends as C D ; thus the line appears 
twice, or it is doubled. The two other lines in the square, 
A C, B D, are formed by the motions of the points at 
the extremities of the moving line. Thus, in passing 
from the straight line to the square the lines double 
themselves, and each point traces out a line. If the 
same procedure holds good in the case of the change of 
the square into the cube, we ought in the cube to have 
double the number of lines as in the square that is eight 
and every point in the square ought to become a line. 
As there are four points in the square, we should have 
four lines in the cube from them, that is, adding to the 
previous eight, there should be twelve lines in the cube. 
This is obviously the case. Hence we may with con- 
fidence, to deduce the number of lines in a four-square, 
apply this rule. Double the number of lines in the pre- 
vious figure, and add as many lines as there are points 
in the previous figure. Now in the cube there are twelve 
lines and eight points. Hence we get 2 x 12 + 8, or 
thirty-two lines in the four-square. 

In the same way any other question about the four- 

What is the Fourth Dimension ? 15 

square can be answered. We must throw aside our 
realising power and answer in accordance with the 
analogy to be worked out from the three figures we know. 

Thus, if we want to know how many plane surfaces the 
four-square has, we must commence with the line, which 
has none ; the square has one ; the cube has six. Here we 
get the three numbers, o, I, and 6. What is the fourth ? 

Consider how the planes of the cube arise. The square 
at the beginning of its motion determines one of the faces 
of the cube, at the end it is the opposite face, during the 
motion each of the lines of the square traces out one 
plane face of the cube. Thus we double the number of 
planes in the previous figure, and every line in the 
previous figure traces out a plane in the subsequent one. 

Apply this rule to the formation of a square from a 
line. In the line there is no plane surface, and since 
twice nothing is nothing, we get, so far, no surface in the 
square ; but in the straight line there is one line, namely 
itself, and this by its motion traces out the plane surface 
of the square. So in the square, as should be, the rule 
gives one surface. 

Applying this rule to the case of the cube, we get, 
doubling the surfaces, 12 ; and adding a plane for each 
of the straight lines, of which there are 12, we have 
another 12, or 24 plane surfaces in all. Thus, just as by 
handling or looking at it, it is possible to describe a figure 
in space, so by going through a process of calculation it 
is within our power to describe all the properties of a 
figure in four dimensions. 

There is another characteristic so remarkable as to 
need a special statement. In the case of a finite straight 
line, the boundaries are points. If we deal with one 
dimension only, the figure I, that of a segment of a 
straight line, is cut out of and separated from the rest of 
an imaginary infinitely long straight line by the two points 

36 What is the Fourth Dimension? 

:at its extremities. In this simple case the two points 
correspond to the bounding surface of the cube. In the 
case of a two-dimensional figure an infinite plane repre- 
sents the whole of space. The square is separated off 
by four straight lines, and it is impossible for an entry 
to be made into the interior of the square, except by 
passing through the straight lines. Now, in these cases, 
it is evident that the boundaries of the figure are of one 
dimension less than the figure itself. Points bound lines, 
lines bound plane figures, planes bound solid figures. 
Solids then must bound four dimensional figures. The 
four-square will be bounded in the following manner. 
First of all there is the cube which, by its motion in the 
fourth direction, generates the figure. This, in its initial 
position, forms the base of the four-square. In its final 
position it forms the opposite end. During the motion 
each of the faces of the cube give rise to another cube. 
The direction in which the cube moves is such that of 
all the six sides none is in the least inclined in that 
direction. It is at right angles to all of them. The base 
of the cube, the top of the cube, and the four sides of 
the cube, each and all of them form cubes. Thus the 
four-square is bounded by eight cubes. Summing up, 
the four-square would have 16 points, 32 lines, 24 
surfaces, and it would be bounded by 8 cubes. 

If a four-square were to rest in space it would seem to 
us like a cube. 

To justify this conclusion we have but to think of 
how a cube would appear to a two-dimensional being. 
To come within the scope of his faculties at all, it must 
come into contact with the plane in which he moves. If 
it is brought into as close a contact with this plane as 
possible, it rests on it by one of its faces. This face is a 
square, and the most a two-dimensional being could get 
acquainted with of a cube would be a square. 

What is the Fourth Dimension ? 17 

Having thus seen how it is possible to describe the 
properties of the simplest shape in four dimensions, it is 
evident that the mental construction of more elaborate 
figures is simply a matter of time and patience. 

In the study of the form and development of the chick in 
the egg, it is impossible to detect the features that are 
sought to be observed, except by the use of the microscope. 
The specimens are accordingly hardened by a peculiar 
treatment and cut into thin sections. The investigator 
going over each of these sections, noticing all their pecu- 
liarities, constructs in his mind the shape as it originally 
existed from the record afforded by an indefinite number 
of slices. So, to form an idea of a four-dimensional figure, 
a series of solid shapes bounded on every side differing 
gradually from one another, proceeding, it may be, to the 
most diverse forms, has to be mentally grasped and fused 
into a unitary conception. 

If, for instance, a small sphere were to appear, this to be 
replaced by a larger one, and so on, and then, when the 
largest had appeared, smaller and smaller ones to make 
their appearance, what would be witnessed would be a 
series of sections of a four-dimensional sphere. Each 
section in space being a sphere. 

Again, just as solid figures can be represented on paper 
by perspective, four-dimensional figures can be represented 
perspectively by solids. If there are two squares, one 
lying over the other, and the underneath one be pushed 
away, its sides remaining parallel with the one that was 
over it, then if each point of the one be joined to the 
corresponding point of the other, we have a fair represen- 
tation on paper of a cube. Fig. 3 may be considered to 
be such a representation if the square C D G H be con- 
sidered to be the one that has been pushed away from 
lying originally under the square A B E F. Each of the 
planes which bound the cube is represented on the paper. 


1 8 What is the Fourth Dimension? 

The only thing that is wanting is the three-dimensional 
content of the cube. So if two cubes be placed with their 
sides parallel, but one somewhat diagonally with regard to 
the other, and all their corresponding points be supposed 
joined, there will be found a set of solid figures, each 
representing (though of course distortedly) the bounding 
cubes of the four-dimensional -figure, and every plane 
and line in the four-dimensional figure will be found to 
be represented in a kind of solid perspective. What is 
wanting is of course the four-dimensional content. 


HAVING now passed in review some of the properties of 
four-dimensional figures, it remains to ask what relations 
beings in four dimensions, if they did exist, would have 
with us. 

And in the first place, a being in four dimensions would 
have to us exactly the appearance of a being in space. 
A being in a plane would only know solid objects as two- 
dimensional figures the shapes namely in which they 
intersected his plane. So if there were four-dimensional 
objects, we should only know them as solids the solids, 
namely, in which they intersect our space. Why, then, 
should not the four-dimensional beings be ourselves, and 
our successive states the passing of them through the 
three-dimensional space to which our consciousness is 
confined ? 

Let us consider the question in more detail. And for 
the sake of simplicity transfer the problem to the case of 
three and two dimensions instead of four and three. 

Suppose a thread to be passed through a thin sheet of 
wax placed horizontally. It can be passed through in two 

What is the Fourth Dimension ? 19 

ways. Either it can be pulled through, or it can be held 
at both ends, and moved downwards as a whole. Suppose 
a thread to be grasped at both ends, and the hands to be 
moved downwards perpendicularly to the sheet of wax. 
If the thread happens to be perpendicular to the sheet 
it simply passes through it, but if the thread be held, 
stretched slantingwise to the sheet, and the h mds are 
moved perpendicularly downwards, the thread will, if it 
be strong enough, make a slit in the sheet. 

If now the sheet of wax were to have the faculty of 
closing up behind the thread, what would appear in the 
sheet would be a moving hole. 

Suppose that instead of a sheet and a thread, there 
were a straight line and a plane. If the straight line were 
placed slantingwise in reference to the plane and moved 
downwards, it would always cut the plane in a point, but 
that point of section would move on. If the plane were 
of such a nature as to close up behind the line, if it were 
of the nature of a fluid, what would be observed would 
be a moving point. If now there were a whole system of 
lines sloping in different directions, but all connected 
together, and held absolutely still by one framework, and 
if this framework with its system of lines were as a whole 
to pass slowly through the fluid plane at right angles to- 
il, there would then be the appearance of a multitude of 
moving points in the plane, equal in number to the number 
of straight lines in the system. The lines in the frame- 
work will all be moving at the same rate namely, at the 
rate of the framework in which they are fixed. But the 
points in the plane will have different velocities. They 
will move slower or faster, according as the lines which 
give rise to them are more or less inclined to the plane. 
A straight line perpendicular to the plane will, on passing 
through, give rise to a stationary point. A straight line 
that slopes very much inclined to the plane will give ri-e 


What is the Fourth Dimension ? 

to a point moving with great swiftness. The motions and 
paths of the points would be determined by the arrange- 
ment of the lines in the system. It is obvious that if two 
straight lines were placed lying across one another like 
the letter X, and if this figure were to be stood upright 
and passed through the plane, what would appear 
would be at first two points. These two points would 
approach one another. When the part where the two 
strokes of the X meet came into the plane, the two 
points would become one. As the upper part of the 
figure passed through, the two points would recede from 
one another. 

If the line be supposed to be affixed to all parts of the 

framework, and to loop over one another, and support 
one another,* it is obvious that they could assume all 
sorts of figures, and that the points on the plane would 
move in very complicated paths. The annexed figure 
represents a section of such a framework. Two lines 
X X and Y Y are shown, but there must be supposed 
to be a great number of others sloping backwards and 
forwards as well as sideways. 

Let us now assume that instead of lines, very thin 
threads were attached to the framework : they on passing 
through the fluid plane would give rise to very small 
spots. Let us call the spots atoms, and regard them as 

A B C D framework, X and Y two lines interlinked. 

What is the Fourth Dimension ? 21 

constituting a material system in the plane. There are 
four conditions which must be satisfied by these spots if 
they are to be admitted as forming a material system such 
as ours. For the ultimate properties of matter (if we 
eliminate attractive and repulsive forces, which may be 
caused by the motions of the smallest particles), are I, 
Permanence ; 2, Impenetrability ; 3, Inertia ; 4, Con- 
servation of energy. 

According to the first condition, or that of permanence, 
no one of these spots must suddenly cease to exist. 
That is, the thread which by sharing in the general 
motion of the system gives rise to the moving point, 
must not break off before the rest of them. If all the 
lines suddenly ended this would correspond to a ceasing 
of matter. 

2. Impenetrability. One spot must not pass through 
another. This condition is obviously satisfied. If the 
threads do not coincide at any point, the moving spotb 
they give rise to cannot. 

3. Inertia. A spot must not cease to move or cease 
to remain at rest without coming into collision with 
another point. This condition gives the obvious condition 
with regard to the threads, that they, between the points 
where they come into contact with one another, must be 
straight. A thread which was curved would, passing 
through the plane, give rise to a point which altered in 
velocity spontaneously. This the particles of matter 
never do. 

4. Conservation of energy. The energy of a material 
system is never lost ; it is only transferred from one form 
to another, however it may seem to cease. If we suppose 
each of the moving spots on the plane to be the unit of 
mass, the principle of the conservation of energy demands 
that when any two meet, the sum of the squares of their 
several velocities before meeting shall be the same as the 

22 What is the Fourth Dimension ? 

sum of the squares of their velocities after meeting. Now 
we have seen that any statement about the velocities 
of the spots in the plane is really a statement about the 
inclinations of the threads to the plane. Thus the 
principle of the conservation of energy gives a condition 
which must be satisfied by the inclinations of the threads 
of the plane. Translating this statement, we get in 
mathematical language the assertion that the sum of 
the squares of the tangents of the angles the threads 
make with the normal to the plane remains constant. 

Hence, all complexities and changes of a material 
system made up of similar atoms in a plane could result 
from the uniform motion as a whole of a system of threads. 

We can imagine these threads as weaving together 
to form connected shapes, each complete in itself, and 
these shapes as they pass through the fluid plane give 
rise to a series of moving points. Yet, inasmuch as the 
threads are supposed to form consistent shapes, the 
motion of the points would not be wholly random, but 
numbers of them would present the semblance of moving 
figures. Suppose, for instance, a number of threads to 
be so grouped as to form a cylinder for some distance, 
but after a while to be pulled apart by other threads 
with which they interlink. While the cylinder was pass- 
ing through the plane, we should have in the plane a 
number of points in a circle. When the part where the 
threads deviated came to the plane, the circle would 
break up by the points moving away. These moving 
figures in the plane are but the traces of the shapes of 
threads as those shapes pass on. These moving figures 
may be conceived to have a life and a consciousness of 
their own. 

Or, if it be irrational to suppose them to have a con- 
sciousness when the shapes of which they are momentary 
traces have none, we may well suppose that the shapes 

What is the Fourth Dimension ? 23 

of threads have consciousness, and that the moving 
figures share this consciousness, only that in their case 
it is limited to those parts of the shapes that simul- 
taneously pass through the plane. In the plane, then, 
we may conceive bodies with all the properties of a 
material system, moving and changing, possessing con- 
sciousness. After a while it may well be that one of 
them becomes so disassociated that it appears no longer 
as a unit, and its consciousness as such may be lost. 
But the threads of existence of such a figure are not 
broken, nor is the shape which gave it origin altered in 
any way. It has simply passed on to a distance from 
the plane. Thus nothing which existed in the conscious 
life on the plane would cease. There would in such an 
existence be no cause and effect, but simply the gradual 
realisation in a superficies of an already existent whole. 
There would be no progress, unless we were to suppose 
the threads as they pass to interweave themselves in 
more complex shapes. 

Can a representation, such as the preceding, be applied 
to the case of the existence in space with which we have 
.'to do ? Is it possible to suppose that the movements and 
changes of material objects are the intersections with a 
three-dimensional space of a four-dimensional existence ? 
Can our consciousness be supposed to deal with a spatial 
profile of some higher actuality ? 

It is needless to say that all the considerations that 
have been brought forward in regard to the possibility of 
the production of a system satisfying the conditions of 
materiality by the passing of threads through a fluid 
plane, holds good with regard to a four-dimensional 
existence passing through a three-dimensional space. 
Each part of the ampler existence which passed through 
our space would seem perfectly limited to us. We should 
have no indication of the permanence of its existence- 

24 What is the Fourth Dimension ? 

Were such a thought adopted, we should have to imagine 
some stupendous whole, wherein all that has ever come 
into being or will tome co-exists, which passing slowly 
on, leaves in this flickering consciousness of ours, limited 
to a narrow space and a single moment, a tumultuous 
record of changes and vicissitudes that are but to us. 
Change and movement seem as if they were all that 
existed. But the appearance of them would be due 
merely to the momentary passing through our conscious- 
ness of ever existing realities. 

In thinking of these matters it is hard to divest our- 
selves of the habit of visual or tangible illustration. If 
we think of a man as existing in four dimensions, it is 
hard to prevent ourselves from conceiving him as pro- 
longed in an already known dimension. The image we 
form resembles somewhat those solemn Egyptian statues 
which in front represent well enough some dignified sit- 
ting figure, but which are immersed to their ears in a 
smooth mass of stone which fits their contour exactly. 

No material image will serve. Organised beings seem 
to us so complete that any addition te them would deface 
their beauty. Yet were we creatures confined to a plane, 
the outline of a Corinthian column would probably seem 
to be of a beauty unimprovable in its kind. We should 
be unable to conceive any addition to it, simply for the 
reason that any addition we could conceive would be of 
the nature of affixing an unsightly extension to some part 
of the contour. Yet, moving as we do in space of three 
dimensions, we see that the beauty of the stately column 
far surpasses that of any single outline. So all that 
we can do is to deny our faculty of judging of the ideal 
completeness of shapes in four dimensions. 

What is the Fourth Dimension? 25 


LET us now leave this supposition of framework and 
threads. Let us investigate the conception of a four- 
dimensional existence in a simpler and more natural 
manner in the same way that a two-dimensional being 
should think about us, not as infinite in the third dimen- 
sion, but limited in three dimensions as he is in two. A 
being existing in four dimensions must then be thought 
to be as completely bounded in all four directions as we 
are in three. All that we can say in regard to the possi- 
bility of such beings is, that we have no experience of 
motion in four directions. The powers of such beings 
and their experience would be ampler, but there would be 
no fundamental difference in the laws of force and motion. 

Such a being would be able to make but a part of him- 
self visible to us, for a cube would be apprehended by a 
two-dimensional being as the square in which it stood. 
Thus a four-dimensional being would suddenly appear as 
a complete and finite body, and as suddenly disappear, 
leaving no trace of himself, in space, in the same way that 
anything lying on a flat surface, would, on being lifted, 
suddenly vanish out of the cognisance of beings, whose 
consciousness was confined to the plane. The object 
would not vanish by moving in any direction, but disap- 
pear instantly as a whole. There would be no barrier no 
confinement of our devising that would not be perfectly 
open to him. He would come and go at pleasure ; he 
would be able to perform feats of the most surprising kind. 
It would be possible by an infinite plane extending in all 
directions to divide our space into two portions absolutely 
separated from one another ; but a four-dimensional being 
would slip round this plane with the greatest ease. 

To see this clearly, let us first take the analogous case 

2ft What is the Fourth Dimension ? 

in three dimensions. Suppose a piece of paper to represent 
a plane. It* it is infinitely extended in every direction, it 
will represent an infinite plane. It can be divided into 
two parts by an infinite straight line. A being confined 
to this plane could not get from one part of it to the other 
without passing through the line. But suppose another 
piece of paper laid on the first and extended infinitely, it 
will represent another infinite plane. If the being moves 
from the first plane by a motion in the third dimension, 
it will move into this new plane. And in it it finds no 
line. Let it move to such a position that when it goes 
back to the first plane it will be on the other side of the 
line. Then let it go back to the first plane. It has 
appeared now on the other side of the line which divides 
the infinite plane into two parts. 

Take now the case of four dimensions. Instead of 
bringing before the mind a sheet of paper conceive a solid 
of three dimensions. If this solid were to become infinite 
it would fill up the whole of three-dimensional space. 
But it would not fill up the whole of four-dimensional 
space. It would be to four-dimensional space what an 
infinite plane is to three-dimensional space. There could 
be in four-dimensional space an infinite number of such 
solids, just as in three-dimensional space there could be 
an infinite number of infinite planes. 

Thus, lying alongside our space, there can be conceived 
a space also infinite in all three directions. To pass from 
one to the other a movement has to be made in the fourth 
dimension, just as to pass from one infinite plane to 
another a motion has to be made in the third dimension. 

Conceive, then, corresponding to the first sheet of paper 
mentioned above, a solid, and as the sheet of paper was 
supposed to be infinitely extended in two dimensions > 
suppose the solid to be infinitely extended in its three 
dimensions, so that it fills the whole of space as we know it. 

What is the Fourth Dimension ? 27 

Now divide this infinite solid in two parts by an infinite 
plane, as the infinite plane of paper was divided in two 
parts by an infinite line. A being cannot pass from one 
part of this infinite solid to another, on the other side of 
this infinite plane, without going through the infinite 
plane, so long as he keeps within the infinite solid. 

But suppose beside this infinite solid a second infinite 
solid, lying next to it in the fourth dimension, as the 
second infinite plane of paper was next to the first infinite 
plane in the third dimension. Let now the being that 
wants to get on the other side of the dividing plane move 
off in the fourth dimension, and enter the second infinite 
solid. In this second solid there is no dividing plane. 
Let him now move, so that coming back to the first 
infinite solid he shall be on the other side of the infinite 
plane that divides it into two portions. If this is done, 
he will now be on the other side of the infinite plane, 
without having gone through it. 

In a similar way a being, able to move in four dimen- 
sions, could get out of a closed box without going through 
the sides, for he could move off in the fourth dimension, 
and then move about, so that when he came back he 
would be outside the box. 

Is there anything in the world as we know it, which 
would indicate the possibility of there being an existence 
in four dimensions ? No definite answer can be returned 
to this question. But it may be of some interest to point 
out that there are certain facts which might be read by 
the light of the fourth dimensional theory. 

To make this clear, let us suppose that space is really 
four dimensional, and that the three-dimensional space we 
know is, in this ampler space, like a surface is in our 

We should then be in this ampler space like beings, 
confined to the surface of a plane would be in ours. Let 

28 What is the Fourth Dimension ? 

us suppose that just as in our space there are centres of 
attraction whose influence radiates out in every direction, 
so in this ampler space there are centres of attraction 
whose influence radiates out in every direction. Is there 
anything to be observed in nature which would correspond 
to the effect of a centre of attraction lying out of our space, 
and acting on all the matter in it ? The effect of such a 
centre of attraction would not be to produce motion in 
any known direction, because it does not lie off in any 
known direction. 

Let us pass to the corresponding case in three and two 
dimensions, instead of four and three. Let us imagine a 
plane lying horizontally, and in it some creatures whose 
experience was confined to it. If now some water or 
other liquid were poured on to the plane, the creatures, 
becoming aware of its presence, would find that it had a 
tendency to spread out all over the plane. In fact it 
would not be to them as a liquid is to us it would rather 
correspond to a gas. For a gas, as we know it, tends to 
expand in every direction, and gradually increase so as 
to fill the whole of space. It exercises a pressure on 
the walls of any vessel in which we confine it. 

The liquid on the plane expands in all the dimensions 
which the two-dimensional creatures on the plane know, 
and at the same time becomes smaller in the third dimen- 
sion, its absolute quantity remaining unchanged. In like 
manner we might suppose that gases (which by expansion 
become larger in the dimensions that we know) become 
smaller in the fourth dimension. 

The cause in this case would have to be sought for in 
an attractive force, acting with regard to our space as the 
force of gravity acts with regard to a horizontal plane. 

Can we suppose that there is a centre of attraction 
somewhere off in the fourth dimension, and that the gases, 
which we know are simply more mobile liquids, expand- 

What is the Fourth Dimension ? 29 

ing out in every direction under its influence. This view 
receives a certain amount of support from the fact proved 
experimentally that there is no absolute line of demarca- 
tion between a liquid and a gas. The one can be made 
to pass into the other with no moment intervening in 
which it can be said that now a change of state has taken 

We might then suppose that the matter we know 
extending in three dimensions has also a small thickness- 
in the fourth dimension ; that solids are rigid in the fourth 
as in the other three dimensions ; that liquids are too- 
coherent to admit of their spreading out in space, and 
becoming thinner in the fourth dimension, under the 
influence of an attractive centre lying outside of our 
space ; but that gases, owing to the greater mobility of 
their particles, are subject to its action, and spread out in 
space under its influence, in the same manner that liquids, 
under the influence of gravity, spread out on a plane. 

Then the density of a gas would be a measure of the 
relative thickness of it in the fourth dimension : and the 
diminution of the density would correspond to a diminu- 
tion of the thickness in the fourth dimension. Could this 
supposition be tested in any way ? 

Suppose a being confined to a plane ; if the plane is 
moved far off from the centre of attraction lying outside it, 
he would find that liquids had less tendency to spread out 
than before. 

Or suppose he moves to a distant part of the plane so 
that the line from his position to the centre of attraction 
lies obliquely to the plane; he would find that in this 
position a liquid would show a tendency to spread out 
more in one direction than another. 

Now our space considered as lying in four-dimensional 
space, as a plane does in three-dimensional space, may be 
shifted. And the expansive force of gases might be 

30 What is the Fourth Dimension ? 

found to be different at different ages. Or, shifting as we 
do our position in space during the course of the earth's 
path round the sun, there might arise a sufficient difference 
in our position in space, with regard to the attractive centre, 
to make the expansive force of gases different at different 
times of the year, or to cause them to manifest a greater 
expansive force in one direction than in another. 

But although this supposition might be worked out at 
some length, it is hard to suppose that it could afford 
any definite test of the physical existence of a fourth 
dimension. No test has been discovered which is decisive. 
And, indeed, before searching for tests, a theoretical point 
of the utmost importance has to be settled. In discussing 
the geometrical properties of straight lines and planes, we 
suppose them to be respectively of one and two dimen- 
sions, and by so doing deny them any real existence. 
A plane and a line are mere abstractions. Every portion 
of matter is of three dimensions. If we consider beings 
on a plane not as mere idealities, we must suppose them 
to be of some thickness. If their experience is to be 
limited to a plane this thickness must be very small 
compared to their other dimensions. Transferring our 
reasoning to the case of four dimensions, we come to a 
curious result. 

If a fourth dimension exists there are two possible 

One is, that there being four dimensions, we have a 
three-dimensional existence only. The other is that we 
really have a four-dimensional existence, but are not 
conscious of it If we are in three dimensions only, 
while there are really four dimensions, then we must be 
relatively to those beings who exist in four dimensions, as 
lines and planes are in relation to us. That is, we must 
be mere abstractions. In this case we must exist only in 
the mind of the being that conceives us, and our experience 

What is the Fourth Dimension? 31 

must be merely the thoughts of his mind a result which 
has apparently been arrived at, on independent grounds, 
by an idealist philosopher. 

The other alternative is that we have a four-dimensional 
existence. In this case our proportions in it must be 
infinitely minute, or we should be conscious of them. 
If such be the case, it would probably be in the ultima e 
particles of matter, that we should discover the fourth 
dimension, for in the ultimate particles the si es in the 
three dimensions are very minute, and the magnitudes in 
all four dimensions would be comparable. 

The preceding two alternative suppositions are based 
on the hypothesis of the reality of four-dimensional ex- 
istence, and must be conceived to hold good only on that 

It is somewhat curious to notice that we can thus con- 
ceive of an existence relative to which that which we 
enjoy must exist as a mere abstraction. 

Apart from the interest of speculations of this kind they 
have considerable value ; for they enable us to express in 
intelligible terms things of which we can form no image. 
They supply us, as it were, with scaffolding, which the 
mind can make use of in building up its conceptions. 
And the additional gain to our power of representation 
is very great 

Many philosophical ideas and doctrines are almost 
unintelligible because there is no physical illustration 
which will serve to express them. In the imaginary 
physical existence which we have traced out, much that 
philosophers have written finds adequate representation. 
Much of Spinoza's Ethics, for example, could be symbo- 
lized from the preceding pages. 

Thus we may discuss and draw perfectly legitimate 
conclusions with regard to unimaginable things. 

It is, of course, evident that these speculations present 

32 What is the Fourth Dimension ? 

no point of direct contact with fact. But this is no reason 
why they should be abandoned. The course of knowledge 
is like the flow of some mighty river, which, passing 
through the rich lowlands, gathers into itself the contribu- 
tions from every valley. Such a river may well be joined 
by a mountain stream, which, passing with difficulty 
along the barren highlands, flings itself into the greater 
river down some precipitous descent, exhibiting at the 
moment of its union the spectacle of the utmost beauty 
of which the river system is capable. And such a stream 
is no inapt symbol of a line of mathematical thought, 
which, passing through difficult and abstract regions, 
sacrifices for the sake of its crystalline clearness the 
richness that comes to the more concrete studies. Such 
a course may end fruitlessly, for it may never join the 
main course of observation and experiment. But, if it 
gains its way to the great stream of knowledge, it affords 
at the moment of its union the spectacle of the greatest 
intellectual beauty, and adds somewhat of force and 
mysterious capability to the onward current. 



|N Persia there was once a king. On one 
occasion when he was out hunting he came 
to the narrow entrance of a valley. It was 
shut in on either side by vast hills, seemingly 
the spurs from the distant mountains. These great 
spurs spread out including a wide tract of land. To- 
wards the entrance where he stood they approached 
one another, and ended in abrupt cliffs. Across the 
mouth of the valley stretched a deep ravine. The king, 
followed by courtiers, galloped along, searching a spot 
where the deep fissure might be shallower, so that 
descending into it he might reach the valley by ascending 
on the opposite side. 

But at every point the ravine stretched downwards 
dark and deep, from cliff to cliff, shutting off all access 
to the valley. 

At one point only was there a means of crossing. 
There were two masses of rocks, jutting out one from 
either side like the abutments of a natural bridge, and 
they seemed to meet in mid air. 

The mass trembled and shook as the king spurred 
his horse over it, and the dislodged stones reverberated 


34 The Persian King. 

from side to side of the chasm till the noise of their 
falling was lost. 

Before the first of his courtiers could follow him one 
of the great piers or abutments gave way the whole 
mass fell crashing down. The king was alone in the 

" So ho," he cried, " the kingdom of Persia is shrunk 
to this narrow spot ! " and without troubling himself for 
the moment how he should return, he sped onward. 

But when he had ridden far into the valley on his 
steed that could outnumber ten leagues in an hour, and 
had returned to the entrance of it, he saw no trace of a 
living soul on the opposite brink of the cleft No sign 
was left, save a few reeds bent down by the passage of 
the mounted train, that any human being had stood on 
the opposite side for ages. 

The evening came on apace. Yet no one returned. 
Again he rode far into the valley. For the most part it 
was covered with long grass, but here and there a thick 
and tangled mass of vegetation attested to a great 
luxuriance of soil, while the surface was intersected here 
and there with rivulets of clear water, which finally lost 
their way in the dark gorge over which he had just so 
rashly adventured. But on no side did the steep cliffs 
offer any promise of escape. 

When the night came on he stretched himself beneath 
one of the few trees not far from the ravine, while his 
faithful horse stood tranquilly at his head. 

He did not awake till the moon had risen. But then 
suddenly he started to his feet, and walking to the edge 
of the cleft, peered over to the land from whence he had 
come. For he thought he heard sounds of some kind 
that were not the natural ones of the rustling wind or 
the falling water. Looking out he saw clearly opposite 
to him an old man in ragged clothing, leaning against 

The Persian King. 35 

a rock, holding a long pipe in his hands, on which he 
now and again played a few wild notes. 

" Oho, peasant ! " cried the king. " Run and tell the 
head man of your village that the king bids him come 
directly, and will have him bring with him the longest 
ropes and the strongest throwers under him." 

But the old man did not seem to give heed. Then 
the king cried, " Hearken, old man, run quickly and tell 
your master that the king is confined here, and will 
reward him beyond his dreams if he deliver him quickly." 

Then the old man rose, and coming nearer to the 
edge of the ravine stood opposite, still playing at inter- 
vals some notes on his long pipe. And the king cried, 
" Canst thou hear ? Dost thou dare to refuse to carry 
my commands ? For I am the king of Persia. Who art 

Then the old man made answer, putting his pipe aside : 
" I am he who appears only when a man has passed for 
ever beyond the ken of all that have known him. I am 
Demiourgos, the maker of men." 

Then the king cried, " Mock me not, but obey my 

The old man made answer, " I do not mock thee ; and 
oh, my Lord, thou hast moved the puppets I have made, 
and driven them so to dance on the surface of the earth 
that I would willingly obey thee. But it is not per- 
mitted me to pass between thee and the world of men 
thou hast known." 

Then the king was silent. 

At length he said, "If thou art really what thou 
sayest, show me what thou canst do ; build me a 

The old man lifted his pipe in both his trembling 
hands, and began to blow. 

It was a strange instrument, for it not only produced 

$6 The Persian King. 

the shriller sounds of the lute, and the piercing notes of 
the trumpet, but resounded with the hollow booming of 
great organ pipes, and amongst all came ever and again 
a sharp and sonorous clang as of some metal instrument 
resounding when it was struck. 

And then the king was as one who enjoys the delights 
of thought. For in thought, delicate shades, impalpable 
nuances are ever passing. It is as the blended strains of 
an invisible orchestra, but more subtle far, that come and 
go in unexpected metres, and overwhelm you with their 
beauty when all seemed silent. And lo, as the strains 
sound, outside palpable, large as the firmament, or real 
as the smallest thing you can take up and know it is 
there outside stands some existence revealed to be 
known and returned to for ever. 

So the king, listening to this music, felt that something 
was rising behind him. And turning, beheld course 
after course of a great building. Almost as soon as he 
had looked it had risen completed, finished to the last 
embossure on the windows, the tracery on the highest 
pinnacles. All had happened while the old man was 
blowing on his pipe, and when he ceased all was perfect. 

And yet the appearance was very strange, for a 
finished and seemingly habitable building rose out of 
waste unreclaimed soil, strewn with rocks and barren. 
No dwellings were near the palace to wait on it, no roads 
led to it or away from it. 

"There should be houses around it, and roadways," 
said the king ; " make them, and fields sown with corn, 
and all that is necessary for a state." 

Blowing on his pipe in regular recurrent cadences, the 
old man called up houses close together, than scattered 
singly along roads which stretched away into the dis- 
tance, to be seen every here and there perfectly clearly 
where they ascended a rising ground. And near at 

The Persian King. 37 

hand could be distinguished fields of grain and pasture 

Yet as the king turned to walk towards the new scene, 
the old man laughed. "All this is a dream," he cried ; 
" so much I can do, but not at once." And breathing 
peals of music from his pipe, he said, " This can be, but 
is not yet." 

" What," asked the king, " is all a delusion ?" and as he 
asked everything sank down. There was no palace, no 
houses or fields, only the steep precipice-locked valley, 
whither the king had ridden ; and his horse cowering 
behind him. 

Then the king cried, " Thou art some moonstruck 
hermit, leading out a life of folly alone. Get thee to 
the village thou knowest, and bring me help." 

But the old man answered him saying, " Great king, I 
am bound to obey thee, and all the creative might of 
my being I lay at thy feet ; and lo, in the midst of this 
valley I make for thee beings such as I can produce. 
And all that thou hast seen is as nothing to what I can 
do for thee. The depths of the starry heavens have no 
limit, nor what I do for thee. Hast thou ever in thy 
life looked into the deep still ocean, and lost thy sight 
in the unseen depths ? Even so thou wilt find no end 
in what I will give thee. Hast thou ever in thy life 
sought the depths of thy love's blue eyes, and found 
therein a world which stretched on endlessly ? Even so 
I bring all to thy feet. Now that all the gladness of the 
world has departed from thee, behold, I am a more 
willing servant than ever thou hast had." 

And again he played, and a hut rose up with a patch 
of cleared soil around it, and a spring near by. 

Then the king said, "Here will I dwell, and if I am 
to be cut off from the rest of the world, I will lead a 
peaceful life in this valley." 

38 The Persian King. 

The sun was rising, the sounds had ceased, and the 
old man had disappeared. 


ME made his way slowly to the patch of cultivated 
ground, he knocked at the door of the hut, and then he 
called out. No answer was made to the sound of his 
voice, he entered, and saw a rude, plain interior. There 
were two forms half lying, half propped up by the walls, 
and some domestic implements lay about. But when 
he spoke to the beings they did not answer, and when 
he touched their arms they fell powerless on the ground 
and remained there. A terrible fear came on the king 
lest he should become such as these. He left them and 
again sought a possible outlet, but fruitlessly. And that 
evening he sought the old man again and inquired what 
sort of beings these were. 

" For though in form and body like children out- 
wardly," said the king, " they do nothing and seem 
unable to move ; are they in an enchanted slumber ? " 

Then the old man came near to the edge of the ravine 
and, speaking solemnly and low, said : 

" O king, thou dost not yet know the nature of the 
place wherein thou art. For these children are like the 
children thou hast known always both in form and body. 
I have worked on them as far as is within my power. 
But here in this valley a law reigns which binds them in 
sleepfulness and powerlessness. For here in everything 
that is done there is as much pain as pleasure. If it is 
pleasant to tread a downward slope there is as much 
pain in ascending the upward slope. And in every action 
there is a pleasant part and a painful part, and in the 

The Persian King. 39 

tasting of every herb the beings feel a bitter taste and a 
sweet taste, so indistinguishably united that the pleasure 
and the pain of eating it are equally balanced. And 
as hunger increases the sense of the bitterness in the 
taste increases, so it is never more pleasant to eat than 
not to eat. Everything that can be done here affords 
no more pleasure than it does pain, from the greatest 
action down to the least movement. And the beings as 
I can make them, they follow pleasure and avoid pain. 
And if the pleasure and the pain are equal they do not 
move one way or the other." 

" This is impossible," said the king. 

" Nay," said the old man, " that it is as I have said I 
will prove to thee." And he explained to the king how 
it would be possible to stimulate the children to activity, 
for he showed him how he could divest anything that 
was done of part of its pain and render it more plea- 
surable than painful. " In this way thou canst lead the 
beings I have given thee to do anything," said the old 
man, "but the condition is that thou must take the painful 
part that thou sparest them thyself." And he bade the 
king cut himself of the reeds that grew by the side of 
the ravine, and told him that putting them between 
himself and any being would enable him to take a part 
of the pain and leave in their feeling the whole of the 
pleasure and the pain diminished by that part which he 
bore himself. 

Then the king cut of the reeds that grew by the side 
of the ravine. He went to the hut where these beings 
lay, and, taking the reeds in his hand, he placed one 
between the child's frame and himself. And the child 
rose up and walked, while he himself felt a pain in his 
limbs. And he found that by taking a pain in each 
part of him the child would exercise that part ; if he 
wished the child to look at anything he, by bearing a 

40 The Persian King. 

pain in his eyes, made looking at it pleasurable to the 
child, and accordingly the child did look at the object 
he wished him to regard. And again, by bearing a 
bitter taste in his mouth he made the child feel eating 
as pleasant, and the child gathered fruits and ate 

Then the king by using two reeds made both the chil- 
dren move, and they went together wheresoever he 
wished them. But they had not the slightest idea of the 
king's action on them. They recognized each other, and 
played with each other. They saw the king and had a 
certain regard for him, but of his action on them they 
knew nothing. For they felt his bearing the pain as this 
thing or that being pleasurable. They felt his action as 
a motive in themselves. 

And all day long the king went with them, leading 
them through the valley, bearing the pain of each step 
so that the children felt nothing but pleasure. But at 
nightfall he led them back to the rude dwelling where 
he had found them. He led them by taking the pain 
from their steps in that direction, and not taking any oi 
the pain from steps in any other direction. 

And when they had entered the dwelling-place he 
removed his reeds from them. Immediately they sank 
down into the state of apathy in which he had found 
them. They did not move. 

And the king at nightfall sought again the side of the 

Gazing across it he saw the sandy waste of the land 
from which he had come, he saw the great stones which 
were scattered about, looking pale and grey in the 
moonlight. And presently in the shadow of a rock 
near the opposite brink he discerned the form of the old 

And he cried out to him, and bade him come near. 

The Persian King. 41 

And when the old man stood opposite to him, he be- 
sought him to tell him how he could make the beings 
go through their movements of life without his bearing 
so much pain. 

And the old man took his staff in his hand, and he 
held it out towards the king, over the depth. 

" Behold, O king, thy secret," he cried. And with his 
other hand he smote the staff which was pointing down 
into the depths. The staff swung to and fro many times, 
and at last it came to rest again. 

Then the king besought him to explain what this 
might signify. 

" Thou hast been," replied the old man, " as one who, 
wishing to make a staff swing to and fro, has made every 
movement separately, raising it up by his hand each time 
that it falls down. But, behold, when I set it in move- 
ment it goes through many swings of itself, both down- 
ward and upward, until the movement I imparted to it 
is lost. Even so thou must make these beings go through 
both pleasure and pain, thyself bearing but the difference, 
not taking all the pain." 

" Must I then," asked the king, "by bearing pain give 
these beings a certain store of pleasure, and then let 
them go through their various actions until they have 
exhausted this store of pleasure ? " 

Then the old man made answer. " Can I have any 
secrets from thee ? Hearken, O king, and I will tell thee 
what lies behind the shows of the world. What I have 
shown thee is an outward sign and symbol of what thou 
shouldst do, but it lies far outside those recesses whither 
I shall lead thee. Thou couldst indeed give these beings 
a store of pleasure, and they would go through their 
actions until it was all spent ; but then thou wouldst 
be as one of themselves. Thou wouldst have to per- 
form the painful part of some action and let them per- 

42 The Persian King. 

form the pleasant part, and thus thou wouldst be 
immersed in the same chain of actions wherein they 
were. For regard my staff as it begins to swing. It is 
not I that make the movement that is imparted to it ; 
that movement lay stored up in my arm, and when I 
struck the staff with my arm it was as if I had let 
another staff fall which in its falling gave up its move- 
ment to the one I held in my hand." 

"Where, then, does the movement go to when the 
staff ceases to swing," asked the king. 

" It goes to the finer particles of the air, and passes on 
and on. There is an endless chain. It is as if there were 
numberless staffs, larger and smaller, and when one falls 
it either raises itself or passes on its rising to another or 
to others. There is an endless chain of movement to 
and fro, and as one ceases another comes. But, O king, 
I wish to take thee behind this long chain and to place 
thee where thou mayest not say, I will do this or that ; 
but where thou canst say, This whole chain of movement 
shall be or shall not. For as thou regardest this staff 
swinging thou seest that it moves as much up as it does 
down, as much to right as to left. And if the move- 
ments which it goes through came together it would be 
at rest. Its motion is but stillness separated into equal 
and opposite motions. And in what thou callest rest 
there are vast movements. It shall be thine, O king, 
to strike nothingness asunder and make things be. Nay, 
O king, I have not given thee these beings in the valley 
for thee to move by outward deeds, but I have given 
them to thee such that thou canst strike their apathy 
asunder and let them live. And know, O king, that 
even as those beings are whom thou hast found, so are 
all things in the valley down to the smallest. The 
smallest particle there is in the valley lies, unless it 
were for me, without motion. Each particle has the 

The Persian King. 43 

power of feeling pain and of feeling pleasure, but by the 
law of the valley these are equal. Hence of itself no 
particle moves. But I make it move, and all things in 
the valley sooner or later move back to whence they 
came. The streams which gather far off in the valley I 
lead along to where they fall into the depths between 
us. There they shiver themselves into the smallest frag- 
rnents,and each fragment I cause to return whence it first 
came. And, O king, in all this movement, since it ends 
where it began, there is no more pleasure than pain. It 
is but the apathy of rest broken asunder. But the par- 
ticles will not go through this round of themselves. I 
bear the pain to make them go through, each one the 
round I appoint it." 

" How then," exclaimed the king, thinking of the pain 
he had felt in directing the movements of the children, 
" canst thou bear all this pain ? " 

" It is not much," answered the old man ; " and were 
it more I would willingly bear it for thee. For think of 
a particle which has made the whole round of which I 
spoke to you it will make this journey if on the whole 
there is the slightest gain of pleasure over pain ; and 
thus, although for each particle in its movement at every 
moment I bear the difference of pain, the pain for each 
particle is so minute that the whole course of natural 
movements in the valley weighs upon me but little. 
And behold all lies ready for thee, O king. I have 
done all that I can do. I can perfect each natural pro- 
cess, each quality of the ground, each plant and herb I 
make, up to the beings whom thou hast found. They 
are my last work, and into your hands I give them." 

And when he had said this, the old man let drop his 
staff, and placing both hands to his breast he seemed 
to draw something therefrom, and with both hands to- 
fling it to the king. 

44 The Persian King. 

For some moments' space the king could distinguish 
nothing, but soon he became aware of a luminousness 
over the mid ravine. Something palely bright was 
floating towards him. As the brightness came nearer 
he saw that it was a centre wherein innumerable bright 
rays met, and from which innumerable bright rays went 
forth in every direction. 

" Take that," the old man cried. " The rays go forth 
unto everything in the valley. They pass through 
everything unto everything. Through them thou canst 
touch whatsoever thou wilt." 

The king took the rays and placed them on his 
breast ; thence they went forth, and through them he 
touched and knew every part of the valley. And think- 
ing of the hut where the children lay, the king perceived 
through the rays that went thither that the walls were 
tottering, and like to fall on the children. And through 
Tiis rays he knew that the children perceived this in a 
dull kind of way ; but since in their life there was no 
more pleasure than pain, they did not feel it more 
pleasant to rise up and move than to be still and be 

But the king through the rays, as before through the 
reeds, took the pain of moving, and the children rose 
and came out of the hut ; and soon they were with the 
king, running and bounding as never children leapt 
and ran, with ecstasy of movement and unlimited 
exuberance of spirit. But as they leapt and ran the 
king felt an increasing pain in all his limbs. Still he 
liked to see them in their full and joyous activity, and 
lie wished them to cast off that dull apathy in which 
they lay. So all through the night he roamed about 
with them thinking of all the wildest things for them to 
do, and leading them through dance and play, every 
movement and activity he could think of. 

The Persian King. 45 

At length the rising sun began to warm the air, and 
the king, exhausted with pain, left off bearing it for 

After a few languid movements the children sank 
down on a comfortable bank into a state of absolute 
torpor. The king looked at them ; it seemed incon- 
ceivable that they could be the same children who had 
been running about so merrily a few moments ago. 
Thus far he had received no advantage from the rays 
the old man had given him, except that he could touch 
the children more easily. 

He turned wearily and looked around. His horse 
stood there. But instead of whinnying and running up 
to greet him, the faithful animal stood still, looking across 
the ravine. 

" Perchance without my burden, and with the strength 
these rays may impart," thought the king, " he might 
manage the leap." 

The horse was standing opposite the remains of the 
natural bridge over which the two had so rashly crossed 
the day before. The king touched the horse with his 
rays. As with a sudden thrust of the spur, the noble 
animal rushed forward and leapt madly from the frag- 
ments of the arch. His fore feet gained the opposite 
brink, and with a terrible struggle he raised himself on 
the firm ground. Then he stood still. With a crash 
the remaining fragments of the bridge fell into the gulf, 
leaving the vast gap unnarrowed at any part. The 
horse stood looking over the ravine. But though the 
king called him by name, the faithful creature who used 
to come to him at the slightest whisper paid no heed. 
In a few moments he galloped off along the track the 
courtiers had pursued. 

46 The Persian King. 


THE king being left thus with the children, applied 
himself to thought. He directed his rays to one of 
the children and caused it to stand up, and, following 
the counsel of the old man, he thought of an action. 
The action he thought of was that of walking, and he 
separated it into two acts; the one act moving the 
right foot, the other act moving the left foot. And he 
separated the apathy in which the child was into pleasure 
and pain ; pleasure connected with the act of moving 
the right foot, pain connected with the act of moving 
the left foot. Immediately the child moved forward its 
right foot, but the left foot remained motionless. The 
child had taken the pleasure, but the pain was left ; or, 
since the king had connected the pleasure and pain with 
two acts, it may be said, had done the pleasant act and 
left the painful act undone. 

After waiting some time to see if the child would 
move, the king took the pain of moving the left foot ; 
instantly the child moved it, and as soon as it had come 
to the ground again it moved the right foot, which was 
the pleasant act. But then it stopped. And by no 
amount of taking pains in the matter of the left foot 
could the king get the child into the routine of walking. 
As soon as he ceased to take the pain of moving the 
left foot, the child remained with the right foot forward. 
At last he removed his attention from the movement of 
the child, and it sunk back again torpor. 

The rest of the day the king spent in reflection, and 
in making experiments with the children. But he did 
not succeed any better. Whatever action he thought 
of they went through the pleasant act, but made no sign 
of going through the painful act 

The Persian King. 47 

When darkness came the king perceived the faint 
luminousness of his rays : unless he had known of them 
he would hardly have perceived it. 

And now he tried a new experiment. He took one 
of the rays, and, detaching it from the rest, he put it 
upon the body of one of the children, going out from its 
body and returning again to its body, so that it went 
forth from the child and returned to the child again. 
He then caused the child to stand up, and again tried 
it with the action of walking. His idea was this : the 
child required a power of bearing its own pain in order 
to go through a painful act, and as the rays enabled 
him to bear their pain, the ray proceeding from the 
child and coming back to it might enable it to bear its 
own pain. And now he separated the apathy into 
pleasure and pain as before. The child moved the 
right foot, and then when it had moved it, he saw that 
it actually began to move the left foot. But it did not 
move it a complete step, and after the next movement 
of the right foot the left foot did not stir. 

Again and again the king tried the children, but his 
attempts came to nothing. One halting step of the 
left foot he could get them to go through, but no 

He spent many hours. Suddenly the cause of his 
failure flashed upon him. " Of course," he said to him- 
self, " they don't move, for I have forgotten to take part 
of the pain. If they went on moving their left feet they 
would have no balance of pleasure." 

And he tried one of them again. The child moved 
the right foot, then began to move the left foot. The 
king now by means of his rays took part of the pain of 
the movement of the left foot, and the child completed 
the step with it. Then of course it moved the right 
foot, for that was pleasant, and again the king took part 

48 The Persian King. 

of the pain of moving the left foot, and the child com- 
pleted its second step. It walked. 

The difficulty was surmounted. Soon both the chil- 
dren were moving hither and thither like shifting 
shadows in the night, and the king felt just a shade of 

The children would come up to him and talk with 
him, if he took the difference of pain which made it 
pleasant for them to do so. But they had no idea of 
his action on them, for by his taking the difference of 
pain they found an action pleasant, and felt a motive 
in themselves to do it, which they did not in the least 
connect with the being outside themselves to whom they 
spoke. They looked on him as some one more power- 
ful than themselves, and friendly to them. 

As soon as he was assured of the practical success of 
his plans, the king let the children relapse into their 
apathy while he thought. He conceived the design of 
forming with these children a state such as he had 
known on earth a state with all the business and affairs 
of a kingdom, such as he had directed before. The 
vision of the palace which the old man had shown him 
rose up. He saw in imagination the fertile fields, with 
the roads stretching between them ; he saw all the 
varied life of a great state. Accordingly from this time 
he was continually directing their existence, developing 
their powers, and learning how to guide them. And 
just as on first learning to read whole words are learnt 
which are afterwards split up into letters by the combi- 
nations of which other words are formed ; so at first 
he thought of actions of a complicated nature, such as 
walking, and associated the moments of pleasure and 
pain with the acts of which such actions were composed. 
But afterwards he came to regard the simpler actions by 
the combination of many of which the beings were made 

The Persian King. 49 

to walk, and with the separate acts of these simple 
actions he associated pleasure and pain. 

And at first the beings were conscious of these simple 
acts and nothing else, but in order that they might carry 
out more complicated actions, he developed the dim ap- 
prehension which they had, and led it on to the conscious- 
ness of more complicated actions. The simplest actions 
became instinctive to these beings, and they went 
through them without knowing why. But if at any 
time the king ceased to take the difference of pain, these 
actions, seemingly automatic as they were, ceased. 

At certain intervals the king found his plans incon- 
venienced. Every now and then the beings went off into 
a state of apathy. Enough pain was borne for them to- 
make it just worth their while to go through the actions 
of each routine. But any additional complication or 
hindrance unforeseen by the king was too much for 
them, and they sank under it. To remedy this he took in 
every action a slight portion of pain more than he had 
done at first. Thus he expended a certain portion of 
pain-bearing power to give stability to the routines. 
And the margin of pleasure over pain thus added was 
felt by the beings as a sort of diffused pleasure in 
existence, which made them cling to life. 

Now in guiding these beings towards the end he 
wished to obtain, the king had to deal with living moving 
beings, and beings whose state was continually changing. 
And this led him to adopt as the type of the activity of 
these beings not a single action, but a succession of 
actions of the same kind, coming the one after the other. 
Thus a being having been given a certain activity, it 
continued going on in a uniform manner until the king 
wished to alter it. 

Again it was important to keep the beings together, 
to prevent their being lost in the remote parts of the 


50 The Persian King. 

valley, and consequently the king tooK, other things 
being equal, a certain amount of the pain of motion 
towards the centre, and took none of the pain in any 
movement away from the centre of the valley. Thus 
the inhabitants had a tendency to come towards the 
centre, for there was a balance of pleasure in doing so, 
and thus they were continually presenting themselves 
to his notice, and not getting lost. 

Of course, if there was\apy reason why he wanted 
them away from the centr^, the king ceased his bearing 
of the pain of motion ttovards the centre, and then they 
were under the other twidency solely, which he imparted 
to them, in virtue.cmnis bearing pain in another respect. 
And in everythingnhat he did the king had regard to 
the circumstances in which the beings were placed, and 
the objects which he wanted to obtain. He did not spare 
any of his pain-bearing power to give them pleasure 
purely as a feeling, but always united the pleasure he ob- 
tained for them by his suffering with some external work. 

And as time went on and the number of the in- 
habitants increased, he introduced greater order and 
regularity into the numberless activities which he con- 
ceived for them. The activities formed regular routines, 
conditioned by the surroundings of the being and the 
routines of those around it. A routine did not suddenly 
cease without compensation ; but if the king wished it 
to stop he let another activity spring up at once in 
place of it, so that there was no derangement. The 
beings gradually became more intelligent, so that they 
could be entrusted with more difficult routines, and 
carried them out successfully, the king, of course, always 
taking the difference of pain necessary to make it worth 
their while. And they even became able to carry out 
single activities on a large scale, involving the co-opera- 
tion of many single routines. For they had a sense of 

Tke Persian King. 51 

analogy, and observing some activity which the king 
had led them through on a small scale, and in which 
they had found a balance of pleasure, they were ready 
to try a similar one on a larger scale. 

There was one feature springing from the advanced 
intelligence of the inhabitants which it is worth while to 
mention. Many of the possible activities which the beings 
could go through, instead of consisting of a pleasurable 
part first and a less painful part afterwards, consisted of 
a painful part first and a pleasurable part afterwards. 
This might happen by the particular arrangement of the 
acts of which the compounded activity consisted, the 
acts having already moments of pain or pleasure affixed 
to them, and happening to occur in such dispositions 
that the first part of the activity was painful, the next 
part pleasurable. 

Now when the intelligence of the inhabitants was 
developed, the king, by leading them to think of such 
an activity, could induce them to go through with it. 
For the idea of the pleasure which would accompany 
the second part of the activity lightened the pain of 
the first. And this, combined with the portion of the 
pain which the king bore, almost counterbalanced the 
pain connected with the first part of the activity. Thus 
the beings were enabled to go through the painful part 
of the activity. But when they came to the second part 
of the activity the creatures were much disappointed. For 
by the law of the valley pleasure and pain were equal 
(except for the small part which the king bore). Now the 
pleasures of expectation had been so great that when the 
time came for the act usually associated in their minds with 
pleasure, the pleasure due had most of it been used up. 

From this circumstance a saying arose amongst the 
inhabitants which was somewhat exaggerated, but which 
had a kernel of truth in what has just been described. 

52 The Persian King. 

The saying was that " The pleasure for which a labour 
has been undertaken flies away as soon as the labour 
has been finished, and nothing is left but to begin a new 
labour." And, again, another saying : " The enjoyment 
of a thing lies in its anticipation, not in its possession." 

All this which has been so briefly described had in 
reality taken a long time. And now fields were culti- 
vated, better houses were built. The inhabitants of the 
valley had increased greatly in number, and were divided 
up into several tribes, inhabiting different parts of the 
valley. But the most favoured position was the centre, 
and for the possession of the centre there were con- 
tentions and struggles. There the king's activity in 
bearing was greatest, and the life was most developed. 

All around the outskirts of the valley dwelt the ruder 
and less advanced people, who were called barbarians 
and savages bv those nearer the centre. 


Now when the king saw the inhabitants becoming more 
like the human beings he had known, he felt that he 
was solitary, and he desired to have some intercourse 
with them. But when he appeared amongst them they 
recognized him at once as some one more powerful than 
themselves, and were afraid of him. In their alarm they 
tried to lay hands on him. When he, to prevent their 
attacks, withdrew his continued bearing the difference of 
pain in their actions, those who were attacking him 
sank into apathy and became as the children whom he 
had first found. 

And a horrible report sprang up amongst the inhabi- 
tants of a terrible being whu came amongst them, and 

The Persian King. 53 

who struck all who looked on him with torpor and 
death. So the king ceased to walk amongst them. 
Still it was long since he had heard the sound of a voice 
speaking to him, and he wished for a companion. He 
sought again the old man, and standing at the edge of 
the chasm he called upon him. 

And the old man appeared. "Art thou weary, O 
king, of thy task ? " 

" Nay," replied the king ; " but I wish to make myself 
known to the inhabitants that I may speak with them 
and they with me." 

And the old man counselled him to give some of his 
rays to one amongst the beings, for then this being 
having these rays and the power of bearing pain for 
another other than himself, would be like the king, and 
being like him would understand him. 
'Now the king sought over the whole of the valley, 
and of all the inhabitants he found one most perfect in 
form and in mind. He was the son of a king, and 
destined to reign in his turn over a numerous people. 
And the king gave him some of his rays, straight rays 
going forth from the prince to others. 

And immediately the prince awoke as it were from a 
dream. And he comprehended existence, and saw that 
in reality the pain and the pleasure were equal. And 
when he had seen this, and knew the power of the rays, 
and how by bearing pain he could make others pass 
through pleasure and pain, and call those sleeping into 
activity ; when the prince knew this, he cried out : 

" One thing succeeds another in the valley ; pain 
follows pleasure, and pleasure follows pain. But the 
cause of all being is in bearing pain. Wherefore," he 
cried, " let us seek an end to this show. Let us pray to 
be delivered, that at last, pain ceasing, we may pass into 

54 The Persian King. 

Thus the prince, apprehending the cause of existence, 
felt that it was pain, and dimly comprehending how the 
king was bearing pain, and himself feeling the strenu- 
ousness of the effort of using the rays for which the 
frame of the inhabitants was unstrung, longed that 
existence itself might cease. 

Yet all his life his deeds were noble, and he passed 
from tribe to tribe, bearing the burdens and calling forth 
the sleeping to activity. 


IT is now the place in which to give a clear account of 
the king's activity, and explain how he maintained the 
varied life of the valley. 

And the best plan is to take a typical instance, and to 
adopt the Arabic method of description. By the Arabic 
method of description is meant the same method which 
the Arabs used for the description of numerical quantities. 
For instance, in the Arabic notation, if we are asked the 
number of days in the year, we answer first 300, which 
is a false answer, but gives the nearest approximation 
in hundreds ; then we say sixty, which is a correction ; 
last of all we say five, which makes the answer a correct 
one, namely, 365. In this simple case the description is 
given so quickly that we are hardly conscious of the 
nature of the system employed. But the same method 
when applied to more difficult subjects presents the 
following characteristics. Firstly, a certain statement is 
made about the subject to be described, and is impressed 
upon the reader as if it were true. Then, when that 
has been grasped, another statement is made, generally 
somewhat contradictory, and the first notion formed 

The Persian King. 55 

nas to be corrected. But these two statements taken 
together are given as truth. Then when this idea has 
been formed in the mind of the reader, another state- 
ment is made which must likewise be received as a 
correction, and so on, until by successive statements 
and contradictions, or corrections, the idea produced 
corresponds to the facts, as the describer knows them. 

Thus the activity of the king will be here described 
by a series of statements, and the truth will be obtained 
by the whole of the statements and the corrections 
which they successively bring in. 

When the king wished to start a being on the train 
of activity he divided its apathy into pleasure and pain. 
The pleasure be connected with one act which we will 
call A. The pain he associated with another act which 
we will call B. 

These two " acts," A and B, which together form what 
we call an " action," were of such a nature that the 
doing of A first and then of B was a process used in the 
organization of the life in the valley. 

Thus the act A may be represented by moving the 
right foot, B by moving the left foot, then AB will be 
the action of taking a step. This however is but a 
superficial illustration, for the acts which we represent 
by A and B were fundamental acts, of which great 
numbers were combined together in any single outward 
act which could be observed or described. 

Suppose for the present that there is only one creature 
in the valley. The king separates his apathy with 
regard to the action AB. Let us say he separates his 
apathy into 1000 pleasure and 1000 pain. Of the 
pleasure he lets the being experience the whole, of the 
pain he bears an amount which we will represent by 2. 
Thus the being has 1000 pleasure and 998 of pain, and 
the action is completed. His sensation is measured by 

56 The Persian King. 

the number 1000 in the first act, and by 998 in the 
second act. 

But the king did not choose to make the fundamental 
actions of this limited and finishing kind. As the type 
of the fundamental activity, he chose an action, and 
made the being go through it again and again. Thus 
the being would go through the act A, then the act B. 
When the action AB was complete it would go through 
an act of the kind A again, then through an act of the 
kind B. Thus the creature would be engaged in a routine 
of this kind, AB, AB, AB, and so on. 

And if the creature had been alone, and this had been 
the sole activity in which it was concerned, the king 
would have gone on bearing 2 of pain in each of these 
actions. The king would have kept the routine going 
on steadily, the creature bearing 1000 of pleasure in 
each A, and 998 of pain in each B. 

At this point it may be asked that an example should 
be given of one of these elementary routines which the 
king set going. And this seems a reasonable request, 
and yet it is somewhat too peremptory. For in the 
world we may know of what nature the movements of 
the atoms are without being able to say exactly what 
the motion of any one is. In such a case a type is the 
only possible presentation. Again, take the example 
of a crystal. We know that a crystal has a definite law 
of shape, and however much we divide it we find that 
its parts present the same conformation. We cannot 
isolate the ultimate crystalline elements, but we infer 
that they must be such as to produce the crystal by 
their combination. 

Now life on the valley was such in its main features 
as would be produced by a combination of routines of 
the kind explained. There were changes and abrupt 
transitions, but the general and prevailing plan of life 

The Persian King. 57 

was that of a routine of alternating acts of a pleasurable 
and a painful kind. It was just such as would be built 
up out of elementary routines, on which the king could 
count, and which, unless he modified their combinations, 
tended to produce rhythmic processes of a larger kind. 
And even the changes and abruptnesses had a recurrent 
nature about them, for if any routine in the valley 
altered suddenly, it was found that there were cases of 
other routines altering in like manner, when the condi- 
tions under which they came were similar. Thus the 
fundamental type of the action which the king instituted 
was that of a routine AB, AB, as described above. But 
there were two circumstances which caused a variation, 
so that this simple routine was modified. 

Firstly, there was not one being only but many. 

Secondly, the king wished to have some of his pain- 
bearing power set free from time to time. He did not 
wish to have to be continually spending it all in main- 
taining the routines he had started at first, and those 
immediately connected with them. 

When he first began to organize the life of the beings 
he did not consciously keep back any of his pain-bearing 
power, but threw it all in the activities which he started. 
Still from time to time he wished to start new activities 
quite unconnected with the old, and for this reason he 
withdrew some of his pain-bearing power, as will be 
shown afterwards. 

There were many beings. The king chose that the 
type of activity in each should be a routine. In that 
way he could calculate on the activity, and hold it in 
his mind as a settled process on whose operation he 
could count. But as the routines of the beings proceeded 
they came into contact with one another, and made, even 
by their simple co-existence, something different from 
what a routine by itself was. They interwove in various 

58 The Persian King. 

ways. Then, in order to take advantage of the com- 
binations of these routines, or to modify them, it was 
necessary to set going other routines. 

In order to be able to originate these connected 
routines the king adopted the following plan. 

In the first action AB he separated the creatures' 
apathy into 1000 pleasure and 1000 pain, bearing 2 of the 
pain himself. The creature thus went through 1000 of 
pleasure and 998 of pain. In the next action AB he did 
not separate the beings' apathy up into so much pleasure 
and pain. He separated it up into 980 pleasure and 980 
pain, that is, each moment of feeling was 20 less in sensa- 
tion than the moments of feeling were in the first action. 

Now it is obvious that if the bearing 2 of pain will 
make it worth while for a being to go through 1000 
pleasure and 998 pain, then the bearing on the king's 
part of i of pain would make it worth while for the 
being to go through 500 pleasure and 499 of pain. 

And a similar relation would hold for different amounts 
of pleasure and pain. Thus clearly for the being to go 
through 980 of pleasure and the corresponding amount 
of pain, it would not be necessary for the king to bear 
so much as when the being went through 1000 of 
pleasure and the corresponding amount of pain. 

Consequently when the king divided the beings' 
apathy into 980 pleasure and 980 pain, it would not be 
necessary for him to bear 2 of pain to make it worth 
the beings' while to go through the action. The king 
would not bear so much as 2 of pain, and thus he 
would have some of his pain-bearing power set free. 
He would have exactly as much as would enable him to 
make it worth a being's while to go through an action 
with the moments of 20 of pleasure and 20 of pain. 

And this with a correction which will come later 
is what the king did. He employed the pain-bearing 

The Persian King. 59 

power thus set free in starting other routines. Thus 
in the routine AB, AB, AB there would be first of all 
the action AB. Then along with the second action 
AB, the king (with the pain-bearing power set free) 
started an action CD the beginning of a routine CD, 
CD, CD. Thus as the first routine went on and came 
into connection with other routines, new and supple- 
mentary routines sprang up which regulated and took 
advantage of the combinations of the old routines. 

The amount of the moments of pleasure in the routine 
CD, was (with a slight correction explained below) 
measured in sensation, equal to 20. Thus the moment of 
pleasure in the first A being 1000, the moment of pleasure 
in the second A was 980, the moment of pleasure in 
the first C was 20 (subject to the correction spoken of). 
Thus the total amount of sensation in the second A and 
and the associated act C, taken together (but for a small 
correction) was equal to the sensation in the first A. 
Hence the three points which were characteristic of the 
activity of the beings in the valley are obvious enough. 

1. There is as fundamental type a routine AB, AB. 
AB, the sensation involved in which goes on diminishing. 

2. There are routines CD, CD, &c., connected with 
AB, AB, in which the sensation which disappears in the 
routine AB, AB seems to reappear. 

3. In the action AB itself there is a disappearance of 
sensation. The sensation connected with A is 1000, that 
connected with B is 998. Thus 2 of sensation seems 
to have disappeared. This 2 of sensation is of course 
the pain which the king bore, and which was the means 
whereby the creature was induced to go through the 
action at all. But looked at from the point of view of 
sensation, it seems like a diminution of amount. This 
diminution of amount, owing to the correction spoken of 
above, was to be found regularly all through the routine.. 

60 The Persian King. 

And now, with the exception of the final correction, 
the theory of the king's activity is complete. There are 
certain mathematical difficulties which render an exhaus- 
tive account somewhat obscure in expression. When 
we take a general survey of a theory we want to see 
roughly how it all hangs together ; but if we mean to 
adopt it, the exactitude of the numerical relations 
becomes a matter of vital importance. 

It must be added that the numbers taken above were 
taken simply for purposes of illustration. In reality the 
pain born by the king was less in proportion. 

The exhaustive account which follows deals with small 
numerical quantities. It had better be omitted for the 
present, and turned to later on for reference. 


We keep for the time being to the numbers used 
above. When the king had enough pain-bearing power 
set free in the second action of the routine AB, AB to 
start another routine CD, of 20 pleasure 20 pain, he did 
not use it all. He only used enough of it to set a routine 
.going the moments of pleasure and pain in which were 
16 in sensation. The routine CD was made up of acts 
with 16 of pleasure and 16 of pain. 

The sensation in the first A was 1000, in the first B it 
was 998, giving a disappearance of 2. In the second 
A it was 980, and in C, which starts concurrently with 
the second A, it was not 20 as might have been ex- 
pected, but 16, giving a loss of 4. The second A is less 
than the first A by 20. Searching for that 20 we find 
1 6 in C. But there has been a disappearance of 4. 

Looking now at the successive acts in the series we 
have in A 1000 sensation, in B 998 sensation, in A and 
C together 996 sensation, 

The Persian King. 


The cause of the loss between A and B has already 
been explained. That between B and the second A with 
C remains to be accounted for. 

It has been already said that the king withdrew some 
of his pain-bearing power from the routine AB and all 
routines connected with it, thus he was enabled to start 
activities altogether unconnected with those which he 
had originated, and was with regard to the products of 
his own activity as he had been at first, with regard to 
the beings in the valley before he started them on the 
path of life. And it was in consequence of his with- 
drawal of his pain-bearing power that the amount of 
sensation in C was not 20 but was less. This loss of 
4 of sensation to the being corresponded to a setting 
free of a certain portion of pain-bearing power on the 
part of the king. And thus as the process went on, a por- 
tion of his power was continually being returned to him. 

In the table below the first line of figures contains the 
amount of sensation in the actions AB, AB. The 
second line of figures contains the amount of sensation 
in the actions CD, CD. The third line of figures relates 
to another connected routine EF, EF, which originates 
in a manner similar to CD. The fourth line of figures 
represents the amount of pain borne by the king, the fifth 
line represents his pain-bearing power set free. 

(i) 1000 998 
A B 

98o 978i*for 
A B 

96o 958 T S-&r 
A B 


16 i5im 

C D 

1(030 T C 6 5 8640 

oitfiro" OTOOOOOO 
C D 


16 isim 

E F 

(4) 2 


T 9 1 _L 360 
1 TTTUTJ " 1 

(5) o 

1 otTO" 

8 _1_ 640 
1000 " TOOOOOO 

62 The Persian King. 

If the total amount of sensation which is experienced 
by the being in the original routine and the connected 
routines in the consecutive stages be summed up, it will 
be found to be 

1000, 998, 996, 994T& QQirfrVfo 
and so on. 

Finally, the proportion of pain borne by the king was 
so small compared with the sensation experienced by 
the being, that A and B were apparently equal in sensa- 
tion. Thus the sensation in the second A and in C 
together becomes apparently equal to that in B. And 
instead of the sensation diminishing quickly as shown 
above, it was only after a great many acts of the primary 
and connected routines had been gone through that any 
diminution of sensation in the form which the being 
could experience it was to be detected Thus, as before 
stated, there was : 

1. A routine of continually diminishing sensation. 

2. Connected routines the sensation in which was ap- 
parently equal to that lost in A. 

3. There was a continuous disappearance of sensation 
from the experience of the beings accompanying every 
step of the routine. The sensation which they could 
experience was less in every subsequent step and con- 
nected steps than in any one in which it was measured. 


vTHE history of the events which took place in the valley 
in their due order and importance must be sought else- 
where. But let us return and look at the condition of 
the valley and its inhabitants. Let us see what has 
become of them after a great lapse of time. 

The Persian King. 63 

It is a fair, a beautiful land. The greater part of it is 
cultivated. There is no war even to the extremest 
confines of the valley there is peace. Passing from the 
remote confines where still dwell a barbarous race, we 
come, as we approach the metropolis, amongst a more 
and more polite and refined people. In the metropolis 
itself the buildings are numerous and of great size. The 
palace which the king saw rise under the old man's music 
is there, but another ruler dwells in it. Near the palace 
are two vast buildings standing on each side of a wide 
open court. There is no other building near save one 
between them, a comparatively small edifice of brick. 
These buildings are the assembly halls of the two most 
important councils in the valley. In the one on the left- 
hand side of the palace met the most distinguished 
of the inhabitants who from a special inclination or 
fitness were entrusted with the regulations about the 
pleasure and pain of the inhabitants. They framed 
the rules according to which each inhabitant must 
conform in his pursuit of pleasure, and they made the 
regulations whereby the whole body of inhabitants were 
supposed to gain an increase in pleasure and to avoid 

In the building on the right hand of the palace met 
those of the inhabitants who had studied the nature ot 
feeling most deeply, and who from temperament or for 
other reasons had in their course of study not paid so 
much attention to whether feelings were painful or 
pleasurable, but who had studied their amount and 
regularity of their recurrence. They were the thinkers 
from whom all the practical inhabitants derived their 
rules of business. They devised the means and manner 
of putting into execution what was decided on in the 
other assembly. They did not often propose any positive 
enactment themselves, but were always able to show 

64 The Persian King. 

how the proposals of the other council could be carried 
into effect. 

Their power was derived in this manner. The king 
had connected the feelings of pleasure and pain with 
certain acts, and had given each being a routine. Now 
as he himself made use of this routine and combined 
the routines of different individuals to bring about the 
results he desired, so also did the rulers of the valley. 
The routines of the individuals were studied and classi- 
fied, and if any work was required to be done, those 
individuals whose routines were appropriate were selected 
and brought to the required spot. Now to effect this a 
careful study of the different routines was necessary, 
and also a knowledge of what stage they were at. For 
it would be no use bringing an individual whose routine 
was almost at an end to a work which was just begin- 
ning. Hence the most delicate instruments and pro- 
cesses had been devised for measuring the amount of 
feeling experienced by any individual, whether of plea- 
sure or of pain, and a careful classification had been 
made of all routines. 

But it is best to study the constitution of the state in 
a regular order, and the questions of pleasure and pain 
considered as such were esteemed the most important. 

The inhabitants knew that they sought pleasure and 
avoided pain, and the great object was to make their life 
more pleasurable. Two means were adopted, the banish- 
ing of the causes of pain, and the obtaining causes of 

By causes of pain and pleasure they meant those 
objects with which the king had associated the feelings 
of pleasure and pain in the equal and opposite moments 
into which he had divided their apathy. 

But in this respect they were in error to a certain 
extent, for it was not so much in respect to things as in 

The Persian King. 65 

respect to actions that the king separated their apathy 
into pleasure and pain. For instance, there was a peculiar 
species of shell which was found in many parts of the 
valley, covered with strange and involved lines and 
marks. Now the king had struck the apathy of the 
inhabitants into two moments with regard to this shell, 
one of pain connected with tracing out the twistings 
and interweavings of the hues on the shell, one of pleasure 
in contemplating the shell when the twistings and inter- 
weavings had been deciphered. Now it was the custom 
of the inhabitants to call the shell in its undeciphered 
condition a painful object, in its deciphered condition a 
pleasant object. And whoever could, would get as many 
deciphered shells as possible and experience the wave 
of pleasure in looking at them. 

Now in the earlier ages those who deciphered the 
shells, or did work of a similar kind, had been forced to 
do it ; they were a kind of slaves dependent on the will 
of their masters, who took away all the pleasures of 
their life. But in these earlier ages a great danger arose, 
for when all the pleasure was taken away by their 
masters, great masses of these slaves sank into apathy, 
and it seemed as if the valley was sinking into deadness. 

Now this was a great terror with the inhabitants whose 
life was pleasurable, and at length they determined that 
there should not be any more of these slaves. But each 
of the inhabitants when he worked for another had to 
have it made worth his while. 

In this way a great diminution took place in the 
pleasure-giving power of the so-called pleasurable things. 
For if a man had had it made worth his while to decipher 
one of these shells, he had had a great deal or nearly all 
of the pain he spent in doing it counterbalanced by the 
pleasure given him to induce him to do it. Hence when 
the shell was handed over there was not much to enjoy 


66 The Persian King. 

in it ; for by the law of the valley the pleasure and the 
pain were equal, and the decipherer, not having gone 
through so much pain on the whole, there was but little 
pleasure to be got. 

In fact, at this time the fashion of filling the houses of 
the more powerful of the inhabitants with the so-called 
pleasurable things had somewhat gone out, and it had 
passed into a proverb, " It is better to decipher your 
own shells." 

Now it may be considered strange how It was that 
some of the inhabitants could get other of the inha- 
bitants to decipher the shells for them at all, or, at any 
rate, to decipher them so that there was any balance of 
pleasure left with the shells at all. But this power on 
the part of some of the inhabitants depended on the 
general action of the king. For by bearing the differ- 
ence of pain in innumerable respects in the life of each 
he made life a pleasure (on the whole) to each, and they 
strove each to preserve their own life which was a source 
of pleasure. And some of the more powerful inhabi- 
tants had the power of denying to the rest, unless they 
laboured for them, the means of continuing to exist. 
Consequently it was possible for things to be obtained 
by the more powerful which had a balance of pleasure in 

But the authorities who had studied the life of the 
valley in relation to pleasure and pain, saw that there was 
a danger in this relation of the more powerful to the less 
powerful. For as the numbers of the inhabitants increased 
the power grew more and more concentrated in the hands 
of a few, and there was a tendency for the inhabitants 
in general to be compelled more and more to go through 
the painful part of actions, leaving the pleasurable parts 
for the more powerful. And every now and then, before 
the council of wise men regulated the matter, great masses 

The Persian King. 67 

of the inhabitants passed off in a state of apathy. So they 
had many laws to restrict the action of the more power- 
ful of the inhabitants ; and, indeed, the more powerful 
of the inhabitants were ready to frame these laws them- 
selves, and were willing to obey them, for they did not 
like to see portions of the inhabitants going off into a 
state of apathy. 

But not only in this respect, but also in every other, 
the wise men regulated the affairs of the valley so as to 
make life more pleasurable. They had severe laws 
against any one who deprived another of pleasure with- 
out his consent, by violence or deceit. They did all 
they could to ward off a state of apathy. But in one 
respect beyond all others they were full of care and 
precaution. And this was in guarding against such 
sources of trouble, anxiety, and pain which could be 
removed from the community as a whole. Anything 
tending to lower the standard of comfort as a whole 
was carefully removed. Irregularities were reduced as 
much as possible ; and, in one respect, a great step had 
been taken. It had not been carried in the council of 
wise men without great opposition, but it had at length 
been passed into law. 

Any child born in the valley which had any incurable 
disease, or any gross deformity, or which by its delicacy 
seemed likely to cause more pain than pleasure in the 
valley, was at once put out of existence. The gain to 
the inhabitants of the valley of this was in their eyes 
immense ; for their sight was offended by no deformities, 
and the painful offices of attending to the sick had 
undergone a considerable diminution since this edict 
had been passed into law. 

The important duty of deciding on the claims of every 
infant that was born to a painless extinction was con- 
fined to a band of inspectors, who stayed for a short 

68 The Persian King. 

time only in any one part of the valley, lest they should 
become biassed by personal acquaintance with the indi- 
viduals for whose children their offices were called into 


PASSING on to the other great building, wnere the other 
wise men meet, it is right to describe what may be 
called the intellectual development as the foregoing 
was the moral development of the valley. The course 
which the opinions of the thinkers in the valley had 
gone through was the following. 

At first they had no clear ideas, but all manner of 
mere opinions and fancies. At last they apprehended 
certain general tendencies such as that towards the 
centre of the valley, and they explained many inclina- 
tions which had before been puzzling to them by this. 
And stimulated by this great discovery they examined 
more and more closely. And they found many special 
tendencies like that towards the centre of the valley, 
which the king had called into existence, and which he 
let go on as a general rule, unless he wished the con- 
trary. And they also succeeded in nearly isolating the 
simplest routines, and so practically could observe the 
type of the king's plan. 

They saw that one act A was succeeded by another 
act B. And not taking into account that one was plea- 
sant the other painful, they measured the amount of 
sensation present in the two acts. And then they took 
the next pair of acts, namely, A and B over again, and 
measured the amount of sensation present in them ; and 
they found that the amount of sensation gradually 
diminished. And at first they thought that sensation 

The Persian King. 69 

gradually came to a stop ; but afterwards they noticed 
that other actions were started in the neighbourhood of 
the routine A B as that diminished in point of feeling. 

Now, of course, these other actions were started by 
the king with the pain-bearing power set free from the 
routine A B, as above described. But not knowing any- 
thing about this action on the part of the king, or about 
the king at all, the conclusion arrived at was this : That 
sensation transmits itself. If it does not continue in 
the routine A B, that part which does not continue 
passes on to the other routines, C D, E F, &c. 

Then they measured very carefully ; and they found, 
as nearly as they could measure, the routines which 
sprang up as the routine A B died away were equal in 
sensation to the loss in the routine A B, A B. And from 
this they concluded that the amount of sensation or 
feeling was constant. They called it living force, and 
said that it must transmit itself and, wherever it ap- 
peared, be equal in its total amount to what it was at 
first. But after a time, with more delicate measure- 
ments and more patient thought, they found that some 
of the sensation was still unaccounted for. 

For consider any routine consisting of the acts A, B ; 
A, B ; A, B. In order to make any pair of acts A, B 
worth while, the king bore a certain amount of pain. 
Referring to the numbers which we took before, if 
there were 1000 of pleasure in A there would only be 
998 of pain in B. Thus the sensation was not equal in 
the two acts A and B. Some of the sensations had 
gone, and the portion of sensation we are now consider- 
ing the portion by which B was less than A had not 
gone in starting other routines. This loss could not be 
accounted for as they accounted for the difference in 
sensation between the first action A B and the second 
action, consisting of the acts A and B in the routine. 

7<D The Persian King. 

There was a loss of sensation which was counter- 
balanced by the gain in sensation in other routines. 

But besides this there was a further loss. Some 
sensation went off, not to be recovered in any routine 
they knew. 

Now it was the bearing on the part of the king which 
produced the appearance of the passing away of sensa- 
tion altogether, so that the act B was less in amount of 
sensation than the act A. But the inhabitants at leas 
the wise ones were firmly convinced that sensatio 
could not be annihilated or lessened. So they came to 
the conclusion that sensation was passing off into a form 
from which it never reappeared, so that it could affect 
them. They conceived it still to exist, but to be irre- 
coverably gone from the life of the inhabitants of the 

Taking the numbers we have taken, and the simple 
instances we have supposed, this course of reasoning 
appears straightforward enough. But in reality so com- 
plicated was the state of things in the valley, and the 
proportion of pain which the king bore in each single 
action so minute, that to have arrived at this result 
implied powers of investigation of no mean order. 

It is interesting to mention the names which these 
investigators gave in the valley. In the performance of 
the pleasant act A, they said that the being acquired 
greater animation. In going through the painful act B, 
they said that he passed into a position of advantage. 
They used the term advantage because, having completed 
the painful act B, he was ready to begin the pleasant 
part of the action A over again. And in this part he 
manifested more animation. 

And now although acts of greater animation and 
greater advantage succeeded one another, and although 
the new total of the sensation in the act of a being was 

The Persian King. 71 

very nearly equalled by that in a subsequent act, still there 
was not they had to confess there was not a com- 
plete equality. Some of the sensation had certainly 
gone from the sphere in which the inhabitants could feel 

We see that this sensation which was gone was in 
reality the pain-bearing of the king, which set all their 
life going. 

But they knew nothing of this, and formed a very 

. different conclusion. They said : " If some of the sensa- 

on is continually going and disappearing from the life 

of the inhabitants of the valley if this is the case, 

although the sensation may not be destroyed, it is 

certainly lost to us." 

And then they thought : " Surely the amount of sen- 
sation must be always the same ; if some%>f it continu- 
ally goes off into a form in which we canrmt feel it, that 
portion which is left behind, and which we feel, must be 
continually growing less." 

Hence they concluded that the sensation in the valley 
was gradually running down. Less and less was being 
felt. After a time, which they calculated with some 
show of precision, all feeling will have left the inhabi- 
tants and gone off in some irrecoverable form. All the 
beings of the valley will sink into apathy. 

Thus coming in the course of their investigations upon 
the action of the king, which was the continual cause 
of all life, they apprehended it as the gradual annihila- 
tion of life. 

The small building between the two council halls 
remains to be noticed. 

Now when the king had connected pleasure and pain 
with different acts to be performed by the inhabitants of 
the valley, he had of necessity to let the pleasant one be 
the one that came first in the order of its possible per- 

72 The Persian King. 

formance. And then by the device of the curved rays 
he had brought it about that the inhabitants went 
through the painful act consequent on the pleasurable 
one, the two together forming the complete action which 
the king had designed. But this chain was not very 
secure. The inhabitants had a tendency to go through 
the pleasurable act and leave the painful act undone. 

Now in things which necessarily concerned their life, 
the king would, by repeatedly bearing the pain of the 
painful act, continually set the beings going again ; for 
when they had performed the pleasant act they were 
landed in a state of torpor, until the pain of the painful 
act had been borne by them or for them. Now if this 
act of which they took the pleasant and left the painful 
part undone was in the main current of their lives, the 
king would over and over again, by bearing the pain, 
bring those who had shirked the painful part into a 
position of advantage again, so that they could begin 
the routine afresh with another pleasant act. And often 
when thus started again they would take to the routine, 
and bear the pain in the painful act themselves. But 
many, after assisting them again and again, the king 
was obliged to let sink into apathy, such namely as 
always left the painful part of the action undone. 

Now the little building was the council hall or inves- 
tigation chamber of the searchers out of new pleasures. 
And by new pleasures they meant something of the 
following kind. With the pleasant and painful acts 
which made up the main routines of their life, it was not 
safe to take the pleasant and leave the painful acts, for 
that gradually led to their sinking into apathy. But 
there were many routines which the king had instituted 
besides the main ones. And if the pleasant part of the 
action constituting these secondary routines were taken, 
then there followed no tendency to lethargy in the main 

The Persian King. 73 

current of their lives, but they simply had a pleasure the 
more. Of course the pain of the painful act had to be 
borne, but they not going through with it left it for the 
king to bear. 

Long ago, through one of the inhabitants of the valley 
with whom he had communicated, the king had sent a 
message, asking the inhabitants not to take the pleasant 
part of an action without the connected painful part. But 
now all memory of this message was lost, and the little 
building had been built, as a council hall or investigation 
chamber for the searching out of pleasurable acts. In 
it all possible novelties of action were discussed. And 
the pleasant parts of them being described, exactly how 
far they were pleasurable, and in what degree they were 
pleasurable, the information was made public throughout 
the land. 


BESIDES these two principal buildings in the metro- 
polis, there were other public buildings devoted to 
various purposes. And some of the most important 
were colleges devoted to the education of the young 

Now there was in the college of applied sensations 
a student who, though outwardly as proficient as the 
average of his companions, was in reality the most 
backward of all. He learned by a kind of rote all the 
doctrines they understood, and he could explain appa- 
rently how one feeling caused another. But in himself 
he had no particle of understanding. He seemed de- 
ficient in the sense of cause and effect which the others 
had. Of this the following instance will suffice to show 
the nature. 

74 The Persian King. 

The king had, in order to prevent the inhabitants 
from straying too far from the metropolis, kept a 
constant watchfulness over their movements, and had 
uniformly taken somewhat of the pain from any effort 
which they made to move towards the metropolis, and 
had not taken any of the pain in efforts whose tendency 
was to remove them to a distance from the metropolis. 
If there was any purpose to be served in going away 
from the metropolis, he took enough pain from these 
movements to make it worth the beings' while to go 
away from the metropolis. But when other things 
were equal, it was a pleasurable thing to go towards 
the metropolis. The king made this general inclination, 
because if it had not been so, beings lying out of the 
way of his immediate attention might have drifted 
away and gone to the confines of the valley, away from 
where the busy life he was calling out was manifested, 
and so have been lost to others and themselves. As it 
was by imparting this general pleasurableness of moving 
towards the metropolis he held all the inhabitants 
together, and knew the direction in which each would 
tend, unless for any special reason he had made it more 
pleasurable for the person to move away from the 

Now, as has been mentioned above, this general ten- 
dency had been observed by the inhabitants ; and they 
knew quite well that every individual tended towards 
the metropolis, and was only prevented from coming 
into it by strong local interests, or by all available posi- 
tions in it or near it being already occupied. If any 
situation was vacant in the metropolis, it was easily 
filled up by those from the surrounding country, for 
they all felt this tendency to press in. 

Now, the learned men in the valley had long recog- 
nized this as one of the most important laws of the 

The Persian Ktng. 75 

valley. And tne students in the college of applied sen- 
sations felt this law to be true law, and anything which 
followed from it they felt to be self-evident. But the 
student of whom we speak had not this happy, settled 
feeling with regard to this law. He could not feel as if 
it were necessarily true. 

One day the head of the college was talking to the 
foremost students those who had nearly finished their 
course and who would take their places in the valley 
shortly and he said incidentally in the course of his 
remarks, that those who were moving away from the 
metropolis were as much attracted to it as those who 
were moving towards it. 

" Why do they move away, then ? " asked the back- 
ward student, who had by great diligence, after a long 
time, plodded his way by force of remembering by heart 
into the top class. He forgot his usual caution and his 
acquired habit of only asking questions he had heard 
asked before in order to refresh his memory with the 
answers he had heard given before. 

The professor frowned at the stupid question. "The 
supposed being," he answered, " while he is attracted to 
the metropolis in accordance with the general law, may 
yet have some stronger inducement at the time to move 
away from the metropolis. That he does move away 
shows of course that his temporary inducement to move 
away is stronger than his permanent attraction towards 
the metropolis." 

The student said that he was obliged for the explana- 
tion. " But " 

" Well ? " said the professor. 

" The only reason you have for supposing that the 
being is attracted towards the metropolis is that he does 
move towards the metropolis. I don't see why you 
should say it was pleasant for him to move towards the 
metropolis when he does not do so." 

76 The Persian King. 

" But we Know," said the professor. 

" No," said the student, " you only suppose ; because 
you find it so on a great many occasions, you suppose it 
is so always. You are like a savage who attacks the 
house of a civilized man. And he tries the window, the 
civilized man meets him there ; so he tries the door, the 
civilized man meets him there ; so he goes back to the 
window, and is met there again. And he concludes 
there are two men in the house ; and after a time he 
concludes there are as many men in the house as there 
are ways by which he tries to get in." 

The student had forgotten himself in speaking like 
this ; and the comparison to a savage, though made 
in haste and in good part as an illustration, offended 
the professor, so he said : 

" You do not believe that the law of attraction towards 
the metropolis is universal, and affects all the inhabi- 
tants ? " 

" I cannot," said the student 

"Then you shall go to a place where you will feel it," 
said the professor. " You will go to-morrow to the ex- 
treme confines of the valley, and stop there until you are 
of a different mind." 

He said this in a superior and gentle manner. But it 
was a terrible blow to the prospects of any student to 
be thus exiled. And yet the professor was within his 
strict legal right, and the student knew it. He had 
avoided this danger all through his college course, and 
now it came with crushing effect on him. For just as 
long ago in the valley they had had doctrines about the 
king, and had punished any one who did not feel them 
as true, and who was found out, so now when all the 
ideas about the king had been disproved, they had severe 
regulations about the belief in the laws. The learned 
-class was a sect of priests, and whoever threatened to 

The Persian King. 77 

bring confusion and trouble by denying any of the 
known laws, and to lead the ignorant people to disregard 
them and deny them, was subject to severe punishments. 
In the case of this student, the error did not so much 
matter, because he had committed his offence in the 
presence of well-instructed people, who would only smile 
at his folly. But he had in his presumption insulted the 
head of the college, and his punishment was universally 
considered to be mild and just. And yet he was not 
altogether in the wrong. For it was not as though the 
king (when he wanted a being to move away from the 
metropolis) took as usual a portion of his effort in going^ 
there ; and at the same time counterbalanced this by 
taking a still larger portion of the pain involved in his 
moving away from the metropolis. By no means. When 
the king willed a man to move away from the metro- 
polis, he let him start afresh, as it were, according to the 
conditions which every being was subject to in the 
valley that it was just as pleasant as painful to move 
in any way, and he took a portion of the pain involved 
in moving away from the city. 

Now the student, when he was sent away, tried ear- 
nestly to see wherein he had been wrong. The place 
where he was exiled was on the confines of the valley, 
where a peaceable race of savages lived, engaged in 
agriculture. In the quiet, monotonous life of the place 
he thought over his whole course of life, but could not 
obtain any different feeling. And while thus buried in 
thought, he fell into the way of going about with the 
savages and doing as they did. Much to his surprise, 
when his preoccupation of mind passed away, he found 
himself singularly at home with them. Their tastes 
seemed to agree with his. And he came to the conclu- 
sion that he was in reality a savage who by some mis- 
take had been admitted to the college. Having formed 

78 The Persian King. 

this conclusion, he threw himself into the life around him 
heartily. In course of time he won the confidence of 
the rude, uncultivated people, and they talked to him 

Many curious traditions were handed down amongst 
them. There were some which proceeded from the time 
when the king had walked and talked with the children 
he called into activity. There were others proceeding 
from times when there had appeared amongst them one 
to whom the king had given some of his rays, so that that 
person had the power of making the pain less in actions 
for others, and of giving them motives to act, and of 
rousing them thus to an active state. And all these 
traditions they told to the exiled student. 

Now their own belief was this. They thought that 
there was a power over them, and in this they recog- 
nized the king ; but how it was that this power 
prompted them they did not know. Yet they connected 
him in some way with pleasure and pain. They thought 
it pained him when they had pleasure, but not in the 
way in which was really the case. They thought simply 
that it was pain to him to see them taking pleasure. 
They thought, moreover, that he would, if they dis- 
pleased him much, take away all their pleasure and 
leave them nothing but pain. 

Now the student saw clearly some errors, some con- 
tradictions in their belief. For instance, he knew that 
beings only followed pleasure, and directly pleasure was 
equalled by pain, sank into apathy, and then gradually 
vanished away. Hence he knew there need be no ap- 
prehension of the power's acting as they thought. But 
the thing they said, that their taking pleasure pained 
this power, struck him. He did not approve the results 
in their life, for it was in consequence very gloomily 
framed, though with a good deal of unconscious cheeri- 

The Persian King. 79 

ness. But he knew as a scientific fact that there was a 
constant diminution of feeling ; and since he also knew 
that beings in the valley did nothing except it was more 
pleasant, he concluded that although pleasure and pain 
might both be disappearing, still pain must be disappear- 
ing to a greater extent. Now since the feeling did not 
become nothing, but passed away out of the perception 
of the inhabitants, it followed that it must pass to some 
being. It did not disappear as feeling, but passed away 
from the sensation of the inhabitants. Is there a being, 
then, he asked himself the power of whom these simple 
folks tell who bears the difference of pain, and so 
makes existence pleasant to us ? And is that the mean- 
ing of what they say that our pleasure pains him ? Is 
it just the truth read backwards the truth, namely, that 
by his taking pain we have pleasures, which they have 
had handed down to them as this that our taking 
pleasure pains him. 

When he had thought thus far he remembered one of 
his books in which the ancient beliefs of the valley were 
discussed. It happened to be one of the books which 
he had brought into his exile with him. He took it down, 
and in the evening set himself to search through it. And 
in a footnote towards the end of the book he read : 

" The existence of a power shaping the valley for the 
good of the beings in it is clearly disproved. First, by 
the amount of suffering there is in the valley. Secondly, 
by the fewness of the types of life, and the constant 
modification of one plan to secure different results 
which would be much better achieved by the use of 
radically different types and means. Thirdly, by the 
absence of any indication of such a power, except in the 
traditions of uncultivated tribes." 

When the student had read this he rose up and paced 
his chamber. For he saw clearly that if it was in bear- 

80 The Persian King. 

ing part of tne pain that the power of the being lay, the 
first of these arguments fell to the ground. The presence 
of the pain in the valley would prove that this power 
took only some of the pain and not all. As to the 
second argument, all it would come to was that the 
being who, bearing pain, gave existence to the inhabi- 
tants, used economy in his actions he chose to effect 
his objects with the least possible expenditure of means. 

Reflecting thus he went out. 

Now it may be considered surprising that the king 
did not communicate in some way with the student, for 
by means of his rays he was in possession of all that 
had gone on in his mind. But the king had found over 
and over again that if he manifested himself to any one 
of the inhabitants of the valley, the effect, though good 
at the immediate time, was most disastrous for the fol- 
lowing time. For the ends he was working towards, 
and leading the inhabitants towards, were much greater 
than any one of them could grasp or conceive. And the 
inhabitants, as soon as they had communication with 
him, at once thought they knew his final will. And 
they were a set most peculiarly stiff in their notions, and 
with the kind of sanction which communication with 
him gave them, even the most absurd ideas if once con- 
ceived took a very long time to eradicate. 

So when the student went out into the open air he 
saw nothing except the stars, and heard nothing except 
the wind. The way was so well known to him, however, 
that he walked on quickly without stumbling in the dark- 
ness. He had not gone far when he saw a kind of 
luminousness. Is it the moon beginning to rise? he 
thought. But he found he had passed the light and was 
leaving it behind. He could not have passed the moon 
thus. He went towards the light, and when he had 
reached it, it seemed like a slender staff of light. He 

The Persian King. 81 

touched it with his hand, and although he did not feel 
anything, yet he could take hold of it, and he walked 
on with the slender beam in his hand. 

He had not gone very far when in his walk he touched 
on something lying in the path. Bending down and 
touching it with his hand he found that it was the form 
of a fellow creature. " He is overcome with fatigue ; 
can I help him along?" he thought. He rose up to 
look round, and let the beam of light which he held in 
his hand touch the prostrate form. " I wish he could 
get up by himself," he thought. No sooner had he felt 
this wish than he had a sensation of pain in his limbs,, 
and the figure rose up. 

" I could not move," it said, " until you came, with all 
my reasons to get along ; the pain was as much as the 

" Who are you ? " 

" I am a wanderer, and am trying to reach the place 
where I was born ; they will help me there." 

Now in the valley there was a certain set of people 
called wanderers, who had proved themselves unfit for 
any real work. These, if inoffensive, were allowed to 
roam about subsisting on charity. The student walked 
alongside this wanderer ; and every step the wanderer 
made he felt a sensation of pain in his limbs. But the 
two walked quickly on till they came to the dwelling he 
had left so shortly before. The student led him in and 
let him rest in his chamber. And then he himself left 
the dwelling again, taking with him a few necessaries. 

The Persian King. 


WHEN he had seen the wanderer safely housed he de- 
termined to go and visit a friend who had lived in a 
town not very far from the metropolis. This friend had 
been his most intimate companion when he first became 
a student, but being older had finished his studies 
sooner, and had left the metropolis before the student's 
misfortune. In leaving his place of exile the student 
rendered himself liable to punishment, and he gave up 
the means of subsistence which had been provided for 
him there. He was obliged to go as a wanderer, and 
trust to the liberality of the people on the way. 

He was hospitably received as a rule. The region was 
remote from the metropolis, the inhabitants were glad to 
talk with a stranger and the wanderers were, in general, 
held to have a stock of exchangeable talk and news. 
But he did not speak with any one of what lay present 
to his mind, till one occasion. 

As he was walking along early in the day, he was 
hailed by an inhabitant who looked like a well-to-do 
farmer. Something in the student's appearance attracted 
him, for, learning that he was on his way to a distant 
town, he asked him to stay and take the first meal of the 
day with him. This inhabitant had been a clerk em- 
ployed in the council of pleasure and pain. But the 
sedentary life had been too trying for him ; he had come 
to live in the country on a small possession of his till he 
had overcome the strain. 

" Did you not find it very dull in the part you come 
from ? " 

" No ; I found that the people had much of interest 
to tell me." 

"They have singular traditions. I remember when 

The Persian King. 83 

a deliberation was held in our council as to whether they 
were pernicious or harmless ; it was decided that they 
were harmless and little likely to spread." 

" I have talked a good deal with them since I have 
lived amongst them, and have come to the conclusion 
that in what they believe a great deal is true." 

" Indeed ! you cannot surely believe that our pleasure 
is distasteful to any being outside us." 

" No ; but I go back to the old notion of which you 
have heard, that there is a being who calls us into being, 
and who is over us ; and I believe that this being takes 
pain, and so makes life pleasurable to us. You know 
that some sensation is passing away, and you know that 
there must be more pain that passes away than pleasure." 

" How can I know that ? " 

" We know that there is not such a very great excess 
of pleasure over pain. Now if in all the course of time 
that has been, the sensation that has been passing away 
was pleasure, there would by this time have been left an 
excess of pain, and before now we should all have sunk 
into apathy. So it is either pleasure and pain mixed 
which passes away, or pain alone. I conceive that it is 
pain alone. These strange doctrines are true, only 
curiously expressed. The being over us is continually 
bearing pain and so making existence pleasant to us, 
thus causing us to move and live. So the pain of our 
life is that remaining pain which he does not take." 

" This seems to me a very dismal doctrine. I can 
imagine some poetry in the idea of a being of infinite 
power, strong and glorious, but none in the idea of a 
suffering being." 

"When you were a child you thought your father 
could do everything ; but as you grew up and found that 
he too had his difficulties, was your regard for him les- 
sened, or your thankfulness for that which he did for you ?" 

" No. And you mean that if we do not regard this 

84 The Persian King. 

being in the same way, granting his existence, still we 
should feel gratitude towards him." 

" Certainly we should feel gratitude to him ; and, con- 
sidering the attitude we have taken towards him, this 
feeling of gratitude comes over us with a kind of revul- 
sion. But besides gratitude I do not see why we must 
lose any other feeling such as you seem to miss. Do 
you not remember how, in the course of the studies we 
have all been through, we were told that there were two 
parts in knowledge one corresponding to reality, one 
introduced by the action of our own minds so that 
certain characteristics which we at first think to be due 
to the nature of things in themselves we find out on 
reflection are only our apprehension of our own mental 
action ? " 

" Yes ; we do not perceive the reality absolutely, we 
apprehend it subject to the mind's mode of perceiving." 

" And of course the mode of the mind's action makes 
it perceive certain qualities as parts of the real existence, 
which do not belong to real existence at all. These 
qualities spring from our mind's own action. In old 
times these qualities were considered to be qualities of 
the reality instead of introduced there. And much of the 
impressiveness of the idea formed of the being of whom 
we speak was due to a mere magnification and extension 
of these qualities qualities which do not correspond to 
anything in reality. So the impressiveness of the idea 
of this being was due to the magnification of qualities 
which originate solely in our minds." 

" This accounts for the idea having faded away. But 
tell me definitely in an instance. Explain by taking 
some particular quality what you mean." 

"I cannot do that, the thought but floats in my mind ; 
still it is always good to embody. Something of this sort. 
When we observe any object we always attribute to it 

The Persian King. 85 

a certain power. Everything has its own powers of 
resistence, of moving, of affecting us in certain ways. 
Thus whatever we apprehend, we apprehend as power- 
ful. Now since this quality of powerful comes in with 
regard to everything, it is probably introduced by the 
mind, and is rather a part of the mental action in giving 
an idea of reality than a quality of reality. If so, when 
we suppose a being to have the quality of ' all powerful,' 
we are not supposing anything at all about the being, 
but are only extending a quality quite barren of any 
correspondence with the absolute nature of things. We 
have left off talking about the being, and are extending 
a conception which springs solely from the only way in 
which we can perceive." 

" Surely you would say that this being was powerful." 
" Of course, if we think of him at all, we must conceive 
of him as powerful ; the nature of our mental action 
demands this. But to dwell on the notion of his power- 
fulness is quite barren, the only subject of thought which 
has content is to inquire what kind of power he has. 
There has been a tendency on the part of those who 
have thought about this being to represent his greatness 
in every respect. But they have not always been judi- 
cious in so doing, because being unable to separate his 
real qualities from those which they attribute to him in 
virtue of their own mode of perception, they have come 
to lay stress on descriptions which on the one hand 
correspond to nothing in reality, and on the other hand 
fail to move those whom they are intended to impress. 
A cloak has been woven. The nature of this being is 
hidden. His nature has been connected with introspec- 
tive questions about the origin of, of all things, the way 
in which we perceive. All this must be dashed aside. 
This being is the cause of all our life, and yet he needs 
your help as you understand help." 

86 The Persian King. 

" I should like to accompany you to your friend and 
hear what he has to sav " 

" Come, certainly." 

So they went together to the town. On the way the 
clerk felt a brightness of existence such as he had not 
enjoyed for a long time. They talked together, and 
confided in one another. At length they came near the 
town where the student's friend lived. They separated, 
the clerk going into the town, the student to the house 
of his friend. On his way there the path led through 
a small wood of very thick growth. Passing along, he 
found that he had left the path. Pausing to reflect in 
which direction he ought to go, he thought he heard a 
sound. It was repeated. Penetrating deep into the 
obscurest part of the wood, he searched till at length he 
found carefully concealed a child, a mere infant. 

The child was nearly perished with exposure. He 
took it up and warmed it. When the child was a little 
better the cause of its having been hidden away was 
apparent. Its breathing was distressed and laboured. 
It suffered under some affection of the lungs, which 
made it gasp at every breath. Still in other respects 
the child was well developed and seemed strongly made. 
It seemed to have been left too long without care to 
recover. The pain of exhaustion from the neglect, and 
added to this the pain of its breathing, was too much 
for it, it was sinking. 

" If I could bear the pain of its breathing," thought the 
student, "it might not sink till I could get some nourish- 
ment for it." 

He looked up, for it seemed to him as if some one 
struck him in the chest. There was no one there. The 
pain continued. He did not drop the child but con- 
tinued on his way to the house of his friend. When he 
got there he noticed a stillness unusual in the houses 

The Persian King. 87 

of the inhabitants. He entered, and was met by his 
friend's sister. He saw at once that something must 
have happened. She took him into a dimly lighted 
room, where he saw his friend lying motionless and his 
face quite white. 

" He has been suffering great pain for long," she said ; 
" it was hoped that if he could bear up the pain would 
have run its course and he would not sink. But all we 
could do was no use." The room was full of all things 
accounted pleasurable, and she looked round as she 
spoke. " It was no good." Taking the child from his 
arms she left him with the form of her brother. 

Sitting down by his side the student felt the strange 
oppression on his chest continue. He went out and 
found that the child had completely revived. It had 
still the appearance of being agonized in its breathing, 
but its eyes were bright, and it laughed. 

" It will be all right soon," said his friend's sister. 

" Tell me what was the matter with your brother." 

When he had heard about his malady he returned to 
the room. After he had sat there for some time he felt 
more and more the sorrow for the loss of his friend, and 
the need of his counsel. This aimless, inert form, this 
lifeless mass, was that which he had come to seek was 
the being with whom he had longed to confer. 

He bent over him. " Could I but snatch him back 
into life ; could I but have one hour's intercourse with 
him. If I had been with him I might have borne some 
of the pain of his complaint before he was overpowered 
with it." He touched the lifeless hands, they were cold 
and damp. He gazed into the expressionless face. He 
seemed to feel the pain of the inner struggle his friend 
had waged against the disease. The quiet of that still 
chamber was gone for him ; in his own person he felt the 
pangs of the struggle for life. A mist came over his 

88 The Persian King. 

eyes, and he sank down holding his friend's hands. 
Suddenly he heard a voice. He rose and looked about 
him. The sound came faintly from the lips of his 

" I have been very ill," were the words he caught. 
" I am so glad you have come ; I was thinking of you in 
my worst moments. You have come just as I am getting 

Indeed the features were regaining expression, the 
hands were warm. It was his living friend again. 

After a few hours he was sufficiently recovered to 
hear about all that had happened. They talked together 
long and earnestly. His friend was convinced. 

"Let us go to your companion," he said. 

They went into the town together. They found that 
the clerk had gone to the magistrates' hall where a trial 
was being held. They did not see the clerk at first, so 
they listened to the proceedings. A woman was brought 
in who had been kept in prison for some days, accused 
of concealing her child. The case was clearly proved. 
The woman received her sentence with an appearance 
of apathy. 

" She will not come out of prison alive," said the 
student's friend, noting her expression. 

But he called out to her from where they stood in the 
body of the court, " Do not fear, your child is safe." 

The woman's face brightened, and she went with her 
jailers buoyantly. 

The magistrate had remarked who it was that had 
spoken, and was about to give orders for the disturber 
of order to be brought up for punishment. But the 
clerk, who was sitting near to the magistrate with whom 
he was acquainted, said : 

" This is the one I have told you about ; pray do not 
punish him." 

The Persian King. 89 

The magistrate accordingly contented himself with 
warning the audience in general terms. 

But he said to the clerk, " Something about him is 
very repulsive to me, do not tell me anything more 
about him." 

The three returned together, and together they de- 
liberated as to how the new idea about the king could 
be made known. It seemed best to go to the metropolis 
and talk with the wisest and most learned there. 

The student asked about the child. His friend's 
sister came and told him that its breathing was not any 
better, but that the child itself was strong and playful. 

" It belongs to the woman who was tried to day," 
said the student, " and must be kept safely till she is 
out of prison." 

His friend after some deliberation gave it in charge 
to a faithful servant to take to the metropolis. A suffer- 
ing child there would be much more likely to be over- 
looked, "and you," he said, "will be able to look after it." 

As the student and the clerk were about to set out on 
their way to the metropolis his friend took him apart. 

" My sister tells me that I had sunk into apathy when 
you came." 

" Yes." 

" And that you called me back ? " 

" Yes." 

" How can I thank you ! had it not been for you I 
should never have enjoyed life again. I am grateful to 

" Do not say grateful to me, but rather to that power 
which does for you all your life that which I do for you 
momentarily now. And even now it is not to me that 
you should be grateful, but to him, for it is only because 
he has enabled me to do so that I have taken of your 

9O The Persian King. 

With this he took farewell of his friend, and with the 
clerk proceeded on their way. 

They had not got very far when a train of servants 
came up behind them. They stood by on one side, but 
from the midst of his attendants a youth stepped 

" I have learned what you have done, and I have over- 
taken you with great haste." 

" What is your wish ? " 

" I want to come with you. I know that you have 
restored your friend from apathy to life. No power is 
so great as that. I have riches in abundance. All that I 
have is at your service ; teach me your power." 

Now in the valley riches meant abundance of pleasant 
things. At the time the student was bearing the con- 
stant pain which he took of the child's breathing, and 
the pain also of his friend's illness. He felt that be- 
fore beginning to take pleasure which was the mean- 
ing of having pleasant things it would be necessary 
to give up the power which he was exercising, so he 
said to the youth somewhat harshly : 

" You cannot compare riches and that which I do, 
nor can you exchange the one for the other. First give 
up all your riches, then you can begin to learn what 
I do." 

The youth turned back, but once again spoke, saying : 

" I will give up a great part of my riches if you will 
teach me." 

" If you want to keep any, however small a portion, 
you cannot do what I do." 

Then the youth with all his attendants passed away. 

The Persian King. 91 


WHEN they came to the metropolis the clerk brought 
many of his acquaintances to see the student. From 
his position in the council chamber, he was able to 
address and induce many of the ablest of the councillors 
to come and inquire. But as soon as they came into 
the presence of the student a sort of constraint sprang 
up between them. They did not take his words as 
having any real meaning. They were occupied all the 
time on speculating what motive it was that made 
him say these things, and as to what kind of differ- 
ence it was which they felt existing between him and 

In fact, as time passed on, no one of any position or 
power would be brought into any sort of approximation 
to him. On the other hand he used to speak continu- 
ally with the poorer people. Those that were sick 
especially delighted in his presence. There seemed to 
be in him a power of stimulating those that were sinking 
into apathy back again into life. Those who were worst 
off in the city seemed to feel when he spoke to them 
a promise of an alleviation of their sufferings. 

One day the clerk asked him 

" How is the child ? " 

" It is well." 

" But it still seems to breathe with as much difficulty." 

" Yes, but see how happily it runs about." 

" How do you manage to preserve it? Any child which 
I have seen would be pining miserably with such an 
affliction. What is the power which the being you tell 
of has given you ? " 

" It is no power in the sense you mean." 

" Surely it must be. Have I not followed you faith- 

92 The Persian King. 

fully and done all I could to get the wisest in the city 
to listen to you ? Surely the time has now come when 
you will tell me what this power is, and, if you can, let 
me share it." 

" You do not know what you ask." 

" Tell me, I pray." 

"It is simply this, when I became aware through 
thought of the being that is over us I had no message 
or command from him. But I found that I could when 
I stood by any suffering being take some of the suffering 
and bear it myself. So as he of whom I tell does with 
us each moment of our lives I do occasionally and in a 
little manner." 

"But what pleasure do you get that makes all this 
worth your while ? " 

" There is no pleasure. I am glad to see the being 
freed from suffering, and living instead of sinking." 

" Do you mean to say that there is nothing to hope 
for ? " 

" I hope the time will come when I shall have a fuller 
knowledge of the being I know." 

The clerk was silent. He went out. While he was 
^till thinking over what he had heard in answer to his 
inquiries, a messenger came to him from the chief of 
the councillors of pleasure and pain, asking him to an 

When the clerk had been ushered into the presence of 
the chief councillor, and was alone with him, the latter 
said : 

'I should like a little quiet conversation with you 
about your companion." 

" I shall be glad." 

" When you gave up your office and retired you had 
no expectation of being concerned in affairs of state 
again so soon." 

The Persian King. 93 

" I did not expect, certainly, and I do not know what 
your meaning may be about my being concerned in 
affairs of state." 

" What I mean is very simple. The continued deliber- 
ations, generation after generation, of the wise men wha 
assemble in the council chamber have been the cause of 
the continued progress of the inhabitants. Nothing is 
done by them hurriedly or violently, but gradually im- 
provement after improvement is worked out. But 
besides this, there have always been at every age 
certain disturbances in the state ; certain doctrines are 
brought forward, and sometimes these tend to good, 
and should be encouraged ; sometimes they are of 
unknown import, and must be studied ; sometimes they 
are against the happiness of the state, and then the 
grave responsibility rests upon us of checking them. 
Now from your position you have more opportunity of 
knowing than any one else in what direction your com- 
panion's doctrines tend. I have sent for you to ask 
yod to share with me this grave responsibility." 

" I do not think I can help you. I am sure he does 
not wish to do any harm. What harm can there be in 
his doctrines ? " 

" It is not so much about his doctrines which I want 
to speak to you as about another subject. Many of 
those who have talked with him have agreed with one 
another in ascribing a singular oppressiveness to his 
presence. The expression was even used by a very 
worthy friend of mine, ' He made me feel like a puppet/ 
Now what right had he to inflict such a sensation on a 
very worthy individual ? I want to ask you yourself if 
you have ever felt this ? " 

The clerk hesitated. 

" At least, tell me, have you ever found it easy tc 
influence him ?" 

94 The Persian King. 

" No ; I do not feel as if I could influence him in the 
least. He seems to lack the ordinary springs of motive." 

" Now, should you say that it would be a gain to the 
community if many should become like him ? Would 
not they be difficult to govern?" 

" Certainly they would be difficult to govern." 

"Would it be a gain in pleasure to the rest of the 
inhabitants or to themselves ? " 

" It would not be a gain to themselves," said the 
clerk, recalling the pain which his companion bore, 
" but it might be good for the rest of the inhabitants." 

"Yes," said the chief councillor, "that is where his 
strength lies ; he is a very skilful physician or an impos- 
tor, and he has the people on his side from the cures he 
has effected. Can you tell me anything about his life ? " 

" I have heard from him that he was a student, and 
was exiled ; and that in his place of exile he found out 
the new doctrines, and he left the place he was sentenced 
to. On his way I joined him." 

"So much we know, and it is within our power, 
according to the regulations, to compel him to go back, 
and to punish him for having left the region he was 
banished to." 

" If you have that power, why do you not send him 
back if you think it would be best for the state for him 
to disappear ? " 

" Ah, my good friend, you have heard a great deal of 
our public deliberations from your place in the council ; 
but now that we are consulting together, I must tell you 
that there are deeper secrets in the art of government, 
which you will readily apprehend. Suppose we arrested 
this individual and sent him away, the people would not 
see the justice of it. They want him now, and they 
would say that the forms of law were being used to get 
rid of him. Of course if his partizans became violent 

The Persian King. 95 

something of this kind would have to be done. But it 
is only a decree that seems just in the eyes of the people 
that we can prudently carry out in such a case without 
attracting even more attention to him than there is at 

The clerk said nothing. The chief councillor went 
on : 

" I am sorry that our conference has come to so little. 
I was hoping that I might have found in you a successor 
to the vacant seat in the chamber. I know you have 
the ability to fill it well. But before the advancements 
are made some proof of the wisdom of the successor is 
required. Hitherto you have not had the chance, but I 
thought that in this difficult case, where you have so 
much better opportunities of observation than any one 
else has, you might have shown your mental power and 
confirmed my opinion of you. Still, no doubt, on some 
future occasion you will have another opportunity when 
this affair, difficult as it is, is forgotten." 

The chief councillor made a sign that the interview 
was at an end, but the clerk remained. 

" All that we want," the chief councillor resumed, " is 
to form an opinion from inside knowledge of whether 
this innovator is likely to cause more pain or more 
pleasure if he gains a hearing. Can you advise us ? any 
particle of knowledge of his inner life, apart from his 
public professions, is valuable." 

" There is a singular fact which I should like to tell 
you of, as it has been somewhat of a burden to me." 

The chief councillor made a sign of assent, and the 
clerk told him about the child, and how it had been 

" And with this child," he said, " he and I sit when 
the day's work is done." 

" It is indeed a strange story," said the chief councillor ; 

96 The Persian King. 

" you are quite right in telling me. I was sure you were 
one on whose discretion confidence might be placed. 
You have given me the highest proof I could have ex- 
pected. The bearings of this matter must be thought 

That evening, as the clerk entered the room where 
they lived, the student was leaning over the child with 
a wearied expression. He went up to him and laid his 
hand on his shoulder. The child looked up at them 
and laughed. It was quite happy despite the apparent 
struggles of its breathing. The student looked at his 
companion's face. His weariness vanished at once, and 
a strong warm light came into his eyes. 

" You seem oppressed, my friend. I know you regret 
the way in which all the wise and important people you 
have brought here look on me, and you must feel some 
sorrow for the partial loss of esteem they have showed 
you in consequence. Can I help you to bear it ? " 

At that moment the door opened, and a messenger 
came in and gave the clerk a sealed packet. He 
opened it and saw that it was his appointment to the 
vacant seat in the council chamber. But his face did 
not brighten. He answered his companion r>oodily, 
and thus the day ended: 


ON the next day the student rose early and went forth 
alone. He did not, as was his wont, go amongst the 
people, but he passed through the streets towards the 
open country. On his way he was stopped by an old 
woman, bent with age and many infirmities. She had 
no place amongst the people, and had so many pains 

The Persian King. 97 

and such a barrenness of existence that any one who 
had thought of her would have wondered that she 
remained alive. 

She stopped him and said, "Master, I have heard 
that you can take my pain. Help me." 

But he answered, looking at her, " No, I cannot, but I 
have a message for you." 

And she said, " A message for me ? I do not know 
any one who would send me a message." 

But he answered, " Nevertheless, I have a message to 
you from my lord, and he bids me thank you." 

She answered, " It cannot be. You must have made 
a mistake." 

But he said, " I have made no mistake ; he thanks 

He could not explain to her how by her bearing pant, 
according to the law of the valley, she took it from that 
which the king bore. Instead of saying that, he gave 
her the message, and somehow the old woman believed it. 

The rest of the day he spent in the open country. 
When he returned it was getting towards dusk. There 
was an unusual movement in the streets. On passing 
into the public market-place he saw a crowd collected ; 
and when he had penetrated to their midst, he saw 
lying on the ground the child he had kept so long. It 
had been lying uncared for and exposed for many hours ; 
and the want of food, the fright, and its gasping breath- 
ing made it the most pitiable object. He at once 
stepped towards it and took it up in his arms. 

" Is that your child ? " said one of the crowd. 

" It is not my own," he answered, " but I take care of 

" Then it is you that are bringing pain upon us ail," 
shouted several voices from the back of the crowd. 
And some one shouted out : 


98 The Persian King. 

" I know you. You pretend to take pain away and 
you really bring much more in secret." 

And moved with a feeling of indignation against the 
one who had caused such a painful object to exist as the 
child was, the crowd closed on him, and barred his way 
to his own place. But they did not lay hands on him. 
As he stood with the child it gradually began to regain 
its composure. But with a sudden movement the crowd 
swept towards the council chamber. And when they 
had come there they demanded that this cruel and 
wicked act of keeping pain in existence should be 

There happened to be several of the chief magistrates 
on the spot, and in obedience to the voices of the crowd 
they proceeded to sit in judgment at once. It was not 
known how the child had come into the streets ; but it 
was admitted by the prisoner to be his doing that it had 
been kept alive. The doctors unanimously said that it 
ought to have been put out of existence directly it was 
born. There was practically no defence. The charge 
of subverting the laws was established. The people 
clamoured for the extreme penalty. The judges passed 
sentence on the student. 

Before morning he was put to death. 

He met his fate without sorrow, even with gladness. 
The pain in his life had for long been as much as he 
could bear. He did not, like the prince of long ago, 
look upon nothingness as the desired end of existence. 
He felt the presence of the one whom he had dis- 
cerned through thought, and this seemed more real to 
him than life or death. 

On the following day, whether in reaction from the 
excitement of the previous evening, or from some other 
cause, an unusual quiet pervaded the streets of the city. 
There was not much discussion as to the event which 

The Persian King. 99 

had happened. The prevailing feeling was one of 
wonder that there should have been so much commo- 
tion about an unimportant affair. For the most part 
before the next evening the whole circumstances were 
on the way to be forgotten. And yet every here and 
there were persons in whose lives the loss of their friend 
was deeply felt. The joy and spring of life seemed gone. 
The poor child lay pale and motionless, save when every 
now an'd then it gasped convulsively for breath. None 
felt the despondency more than the clerk. The interest 
and value of life seemed to have gone. He did not care 
for his new honours. 

That day some most unexpected news went through 
the town. The chief of the council of sensation had 
sunk into apathy. He was in the prime of his life. It 
was most unexpected. Every one was astonished at 
the news, but were still more astonished at how little 
they felt concerned. 

Following on these tidings came others. Many of 
the inhabitants of the metropolis whose lives were most 
strenuous suddenly succumbed. The clerk had made 
up his mind to go into the country. But tidings came 
from there also that the poorer labourers, and those who 
were exposed to the fatigue of long journeys or exposure 
were in many cases sinking. The wave of torpor seemed 
passing over the whole valley and not to be confined to 
the metropolis. The rich and unoccupied classes only 
were comparatively unaffected. They betook them- 
selves to the store of enjoyable things at their service, 
and so replaced the natural spring of life which seemed 
tending to fail in every one. 

On the confines of the valley, where the ravine struck 
it vast depth between this land and that, vast and end- 
less as the sea stretched the plain whence the king had 
come. It was struck silvery grey by the light of the 

ioo The Persian King. 

moon, dark shadows marked the nearer strands, and 
gradually the rocks which cast them showed their sharp 
outlines, hardly distinguishable from the ground out of 
which they rose. 

Over the great gulf Abated the sounds of a pipe, the 
strains were low, winning the soul with the sweetness of 
an unearthly melo&y, throbbing as with a call to a 
distant land aw^avjand beyond. 

And when, ttye eye found the source of the sounds, 
there stood, once more, solitary in the unten anted vast, 
the king's devoted friend, the same old man who before 
had hailed him. Gradually the music sank lower and 
lower, till at length silence spread in folds unruffled. 
Then on the edge of the valley a form appeared. It 
came and seemed to gaze across the gulf, standing 
motionless and intent. At length a voice came. 

" Art thou there ? " 

" Yea, O king, what wouldst thou ? Art weary ? " 

No answer came. 

Then the old man spoke. " Behold the roads where 
they stretch gleaming white in the moonlight ; behold 
the fields, the villages ; see in the distance the great walls 
of the palace. Have not these risen up for thee, O 

Then the king made answer : " I am weary." 

Suddenly the old man raised his pipe with both his 
hands to his lips. Wave after wave of triumphant 
sound pealed forth. Great harmonies such as marching 
nations might hear and rejoice, noble notes of unbounded 

Then, crossing by an unknown way, he came and 
stood by the king's side. After a while the two moved 
on together, and by a secret path passed away from the 
valley whither I know not. 

As soon as the king had departed from the valley the 

The Persian King. 101 

beings in it began to sink into the same state of apathy 
as those were whom he had first found there. Those 
who sank first were the ones in whose lives the stress of 
labour or thought was the most intense, for they first 
felt the loss of that bearing of pain by one beyond 
themselves which gave them a difference of pleasure. 
And slowly as the accumulated enjoyment was ex- 
hausted, a chill death in life crept over the land. Tis 
useless to ask after the fate of any one of those that 
were there, for each was involved in the same calamity 
that overwhelmed all. Every hand forgot its cunning. 
The busy hum of life in the streets was hushed. In the 
country the slowly moving forms gradually sank to rest. 
At every spot was such unbroken quiet as might have 
been had all the inhabitants gone to some great festival. 
But there was no return of life. No watchful eye, no 
ready hand was there to stay the slight but constant 
inroads of ruin and decay. The roads became choked 
with grass, the earth encroached on the buildings, till in 
the slow consuming course of time all was buried 
houses, fields, and cities vanished, till at length no trace 
was left of aught that had been there. 



THERE are certain respects in which our world resembles 
the valley. Instead of regarding pleasure, pain, and 
feeling, let us examine the world we live in with regard 
to motion in one direction and another, and in respect 
of energy. 

If we observe the movements which go on in the 
world, we find that in great measure they consist of 
movements which if put together would neutralize each 

A pendulum swings to and fro. If tne two move- 
ments took place at the same time the pendulum would 
be still. Taking a more ample motion that of the 
earth round the sun. The earth moves in the course of 
its orbit as much towards the sun as away from it, and 
as much towards the east as towards the west. If all 
the motion were to be gone through at one and the 
same time the earth would not move with regard to 
the sun. 

Again, if we notice what goes on on the surface of the 
earth, we see that there is a motion of rising up and 
of sinking down. There is an approximation of the 
chemical elements into some compounds, and a separa- 
tion of them again. Of all the myriad processes which 

Our World. 103 

go on, the swing of a pendulum is the type. But the 
downward swing may be very different to the upward 
swing. It may be that the downward swing is repre- 
sented by the violent action of the chemical affinities in 
a charge of gunpowder when exploded, and the upward 
swing may be represented by the swift motion imparted 
to a cannon ball, and the swift motion of the cannon 
ball in its turn comes to rest, and as it comes to rest 
slowly or quickly other changes take place. 

And what we notice in our world is similar to what 
the inhabitants of the valley noticed about pleasure and 
pain that they do not neutralize one another as a 
matter of fact. 

The contrary motions on the earth which, if they were 
put together, would neutralize one another, do not as a 
matter of fact neutralize one another. We call motion 
in one direction positive in the opposite direction 
negative. But in the world as a matter of fact positive 
and negative motion do not together come to nothing. 

As in the valley the states of pleasure and of pain did 
not coalesce into a state of apathy, but always succeeded 
one another, in simple or complicated fashion, so on 
the earth it is impossible from two opposite moving 
bodies to get stillness. If the two come into contact in 
opposite directions the movement does not stop, but 
makes its appearance in an alteration of the shape of 
the bodies, in a disturbance of their particles, or in some 
such fashion. 

Again in the valley, by measuring the pleasure and 
pain simply as feeling, and not taking into account 
whether it was pleasure or pain, the inhabitants found 
that the feeling was always the same in amount. 

So we On the earth, measuring the amount of move- 
ment, and leaving out of account whether it is positive 
or negative, come to the conclusion that the quantity of 

IO4 Energy. 

movement, reckoned in the way in which we call it 
energy, is always the same. The principle of the con- 
servation of energy has become a fundamental one in 

But besides the discovery that the amount of sensation 
as such was always constant, the inhabitants of the 
valley discovered that a portion of the sensation was 
passing away from a form in which they could feel it. 

And there is an analogous discovery in science. We 
know that a portion of the energy of our system is 
passing away. It is not being annihilated, but is dis- 
appearing. With the energy which can be collected 
from the falling of a stone, the same stone cannot be 
raised to its former level again. Some of the energy 
has disappeared from the form in which it can be known 
as the energy of moving masses. The energy has in 
some measure irrecoverably passed off in the form of heat. 

Hence, just as the inhabitants of the valley came to 
the conclusion that in point of sensation they were 
"running down," and that after a time all sensation 
would have passed away from the form in which they 
could feel it, so we have come to the conclusion that 
the energy of the system in which we live is running 
down, that the energy is passing out of the form in 
which it can be manifested as moving masses, that 
finally all movement of masses will come to a standstill, 
and there be nothing left save motionless matter, with 
warmth equally diffused through it. 

Now in coming to the conclusion about the valley, 
that the amount of sensation was gradually passing away, 
the inhabitants, as we have seen, had come upon the 
very secret and cause of all the life in the valley. But 
coming upon it from the outside they had not recognized 
the significance of what they had found. The cause 
and prime mover of all their existence indicated itself to 

Permission. 105 

them, coming thus upon it, as a process whereby all that 
went on was doomed to a distant but certain extinction. 

Now, is this process of the passing of mechanical 
energy into the form of heat to be interpreted by us in 
a way analogous to that in which the inhabitants of the 
valley could have interpreted the process they found ? 

In this cessation of sensation in the form in which 
they could experience it lay the central fact of the life of 
the valley. Has this passing away of energy from the 
form in which we can experience it an analogous signifi- 
cance to us ? 

In order to examine into the possibility thus suggested 
there are four convergent lines of thought which it will 
be well to follow up separately. Each of these lines of 
thought bears in an independent manner on the central 
question the significance of the passing away of energy. 
These lines of thought may be connected with the 
following words, which indicate their significance : (i) 
Permission ; (2) Causation ; (3) Conservation of Energy ; 
(4) Level. 


WHEN we observe any movement taking place we ask 
what is the cause of it ? what is the force which produces 
it ? But surely, if we confine our inquiry to this point, we 
have made an omission. That we are not conscious of 
having made an omission may perhaps come from our 
living in the air which yields so easily to any moving 
body. If we lived in a rigid medium we should, when 
we became aware of any moving body, ask two questions. 
First, what urges it along ? secondly, what prepared the 
channel for its motion ? 

But seriously, without laying any stress on the above 

1 06 Permission. 

illustration, we see that to every movement two condi- 
tions are necessary : a pushing and a yielding, a force 
and a permission. If the particles of the air could not 
yield, a pendulum could not swing through it. If again 
the air could not pass on the motion it has received, it 
could not yield to the motion of the pendulum. 

Now since every motion requires a permission, we are 
led to ask the question, What is the ultimate per- 
mission ? What again is that which by yielding allows 
motion at all to take place ? 

If we trace any movement scientifically we find an 
indication of what the ultimate permission is. 

A body swings through the air. Currents in the air 
are set up. These currents impinge on the objects with 
which the air is in contact, and in them produce heat 
producing heat also by friction with other portions of 
the same air. Every motion thus passes off finally, at 
however long an interval, in the form of heat. Motion 
may reappear as motion through myriads of phases, but 
at each change of form some of it passes off into the 
form of heat, and finally all passes off into the form of 
heat. Thus, unless matter admitted of being warmed, 
there would be no ultimate permission. A motion once 
started would never come to rest. Or, rather, no motion 
could take place at all. 

The tendency of the above remarks is to avoid the 
conception of there being absolute laws of motion, true 
of bodies when surrounded by no medium, modified 
when a medium is present. Surely such a conception is 
an instrument of the mind for exploring nature, not an 
absolute fact in nature. The abstract laws of motion 
are mental aids in creating knowledge ; like scaffolding 
for the builder, even from their very usefulness they 
have probably but little to do with the permanent 

Permission. 107 

This passing into the form of heat supplies a place 
analogous to that of the " void " in the speculations of 
the Epicurean philosophers. They argued that motion 
was not possible without a void. Given a void, some- 
where into which matter could move, then any amount 
of motion could be accounted for. But without a void 
into which a portion of matter could move, how was it 
possible for motion to begin ? 

Thus repeating their inquiry with our altered concep- 
tions, we ask this question about motion, or energy 
(which is a particular way of reckoning motion). 

Unless motion can in some way pass off, how can 
there be all these transformations of energy ? 

Now the ultimate transformation of all energy of 
motion is into the form of heat. In this change into the 
form of heat is to be sought the ultimate permission 
which makes all transformations of energy, all motions, 
possible. It is this being acted on of the finer particles 
of matter which permits the movements of the larger 

This passing of energy into the form of heat must not 
be regarded as a side circumstance, as less essential to- 
the laws of nature than that law which we call the con- 
servation of energy. It is at the same time the end of 
every motion, and that which makes every motion 

The passing of energy into the form of heat takes 
place in that which we call friction, and in all those 
modes in which any movement is brought to a stand- 
still. But so far from these being simply " hindrances " 
to motion, it is through them that we learn that which 
makes motion possible. It is with us as with the inhabi- 
tants of the valley, the gradual cessation of feeling from 
their life and the modes in which it ceased were the way 
in which they regarded the action of the king who was 

[o8 Causation. 

the cause of all. We have thought of motion as a tning 
in itself impaired by the multitudinous obstacles it meets 
in the world. Let us look on the circumstances more 
impartially. Let us look on them as something co-equal 
with motion. Let us find in that mode whereby all 
motion comes to an end the originating cause also 
whereby all motion comes to be. 

The passing of the motion of masses into the form of 
heat is the ultimate permission. 


IF we reflect cautiously on the history of our opinions, 
we find that we often fall into error in respect to our 
freedom in attributing causes. If we are unfortunate we 
are apt to look on our neighbours, or the world, or, if we 
are of a self-depreciatory turn of mind, ourselves as the 

Again in past times people really felt sure about 
certain things being causes which we now know had a 
very slight connection with the result. Incantations 
have been supposed to have an effect on physical phe- 
nomena, such as eclipses. Numbers and their properties 
have really been conceived as the causes of the modes of 
existence. Ideas have been supposed to have causative 
power over the order of the world. 

We should be very careful in attributing the notion of 
causation. If we see a stone lying on the ground, and 
proceed to pick it up by the strength of the arm, we say 
that the exertion of the arm is the cause of the stone 
being lifted. But in this respect even we are too hasty. 
The arm may exert itself and yet the stone not be lifted 
up if it is too heavy. All that we can say about it is that 

Causation. 109 

if the stone is lifted, a certain set of muscular actions 
has gone on in the arm, and a certain movement of the 
stone has taken place. If we look closely at the matter, 
the movements in the arm are related to the movements 
in the stone in a strictly measurable way. There has 
been so much exertion corresponding to the weight of 
the stone. But suppose the arm had done anything 
else, there would have been the same relation traceable 
between the movements in the arm and the actions 
which followed its movements. The energy spent by 
the arm would be equal to the energy imparted to the 
object moved, whether it be a stone sent flying through 
the air, or one lifted to a higher position (bearing in 
mind always the small quantity of energy passing off in 
the form of heat). 

It does not seem advisable that the notion of cause 
should be brought in to denote the relation of the move- 
ment of the arm and the movement of the stone. These 
are two sets of actions between which the regular rela- 
tions which hold good between the consecutive states of 
moving systems hold good. 

The notion of " cause " should rather be applied to 
that act of the will whereby the movements of the arm 
are connected with the movement of that particular 
stone rather than the movement of any other object. 

We are the cause of the actions we will. The notion 
of cause is derived from our " will " action, and the notion 
of cause ought to be kept to this connection. 

All that goes on outside us can only be apprehended 
as consecutive states following on one another. Between 
certain sets of consecutive events we notice that the same 
relation holds good which we have observed in other 
consecutive states. If some water is heated in England 
it passes off into steam ; if water is heated in another part 
part of the world it also passes off into steam. There is 

no Causation* 

an exact analogy in the behaviour of water under the 
action of heat wherever we observe it. But all that we 
have obtained as knowledge is the fact that we may 
practically be confident of an analogous behaviour on 
the part of water wherever circumstances are similar. 
We may use the expression that heat is the cause of 
water boiling for convenience. But the expression 
should not be used as containing any deep meaning. 
To say one external event is the cause of another is 
to put an absolutely unknown and spiritual relation in 
place of impartial observation. 

To cause a motion is the name for the action of our 
soul on matter a thing shrouded in mystery. To be 
the antecedent in a chain of movements is the fact which 
we can observe about any movement in the external 
world. We cannot strictly say what movements of 
gases, water, &c., cause this volcano. We can only say 
what movements of gases, water, &c., precede this 
volcanic eruption analogous to movements which have 
preceded other volcanoes. 

There are invariable sequences in the external world to 
which we do not affix the notion of cause and effect day 
and night, summer and winter. Why we should do so 
in any case is not clear, except that by familiarity and 
mystery the sequences have become to us something like 
our own will action. Indeed, is it not the case that when 
we can trace intermediate links we say so and so comes 
from so and so in such a manner. But when no inter- 
mediate links can be traced we say one event causes 

If, however, we omit the feeling of causation from the 
external chain of events, it does not follow that there is 
no causation to be apprehended in the external world. 

Let us not introduce the notion of causation at hap- 
hazard. But if we find in the external world signs of 

Conservation of Energy. 1 1 1 

an action like our own will action, let us then say, Here 
is causation. 

The inhabitants of the valley would not have been 
right in saying that one act of a routine caused another: 
But they were right in saying that the amount of sensa- 
tion was constant, and that some of it passed off in a 
form in which they could not feel it. 

And so let us not say that one action causes another. 
Let us not say, for example, that the downward swing of 
a pendulum is the cause of its upward swing. But let 
us simply say that the one follows the other ; that the 
amount of energy present is the same except for the 
small portion that passes off into the form of heat. 


SUPPOSE certain sets of numbers were being presented 
to us one after the other, and amongst these three con- 
secutive sets were the following. First set : 3, 5, 6. 
Second set : 8, 2, i, I. Third set : 7, 4, 2, I. 

A little consideration will show us that there is a 
certain uniformity in these sets. 

Take the square of each of the numbers in the first 
set and add them together, the result is 70. Thus 
3 2 + 5 2 + 6 2 = 9 + 25 + 36 = 70. 

The sums of the squares of the numbers in the second 
set come to the same. 8 2 + ( 2) 2 + (- i) 2 -f I 2 = 64 
+ 4 + i + i = 70. Also in the third, 7 2 4- 4 2 + 2 2 + 
(- i) 3 = 49 + 16 + 4-1- i = 7> and so on. 

Having noticed this we should regard it as a purely 
formal law, having nothing to do with why the num- 
bers were presented to us. But we should consider 
it likely that it would characterize all the numbers that 

H2 Conservation of Energy. 

were presented to us. And if this expectation were 
found to be realized, we should after a time feel a cer- 
tain assurance that the next set of numbers presented 
would satisfy the same law. If this assurance was 
indefinitely satisfied we should get to regard the satisfy- 
ing this law as an invariable condition of the numbers 
presented. But we should never regard this purely 
formal law that is, a law about the particular charac- 
teristics of the numbers we should never regard this 
formal law as the cause of the next set of numbers 
appearing after the first had gone. 

When, however, we talk about the conservation of 
energy we are apt to think of it as more than a merely 
formal law, more than a statement about numbers which 
has been found to hold true. 

Yet it is no more. The law of the conservation of 
energy asserts that in any system in motion the sum of 
the squares of the velocities of the particles at any one 
moment is equal to the sum of the squares of the velo- 
cities of the particles at the next moment. 

The conservation of energy is but a mode of reckon- 
ing motion, by which it is found to be constant in all 
changes of a system. The system must embrace all 
the particles concerned in the motion. It may be made 
as large as we like. 

The principle of the conservation of energy as here 
stated is confined to the case of moving bodies. Some- 
times the energy is said to disappear from the form of 
motion and become potential energy. That case will be 
treated under the fourth consideration of level, but it 
introduces no alteration in what has been said. 

As to the practical truth of the law of conservation of 
energy there can be no doubt ; nor as to the value of 
the results obtained from tracing its validity in obscure 
actions. But there is nothing final about it It is a 

Conservation o/ Energy. 113 

numerical statement of extreme value, and it introduces 
a mode of reckoning by which motion can be looked 
upon as indestructible as matter is. 

There is a possible objection to the law of conserva- 
tion of energy. 

It is no less a law in nature that in every one of 
a series of changes some of the energy passes off into 
the form of heat. Now heat is reckoned as a mode of 
energy. And there is in science a method of calculat- 
ing how much energy any given quantity of heat is 
the equivalent of. And this equivalence is calculated 
on the supposition that no energy is lost. When heat 
is produced and motion passes away, the proportion 
between the motion that disappears and the heat that 
appears is represented by a number calculated on the 
assumption that no energy is lost. Thus whenever 
any quantity of energy takes the form of heat, the quan- 
tity of heat which is produced is exactly given by the 
calculation. But the reverse process is not possible. 
It is not possible to turn back all the energy in the form 
of heat into the form of motion. Consequently it can- 
not be proved that the energy in the form of heat would, 
if all turned into motion, produce as much motion as 
that from which it was produced. There may be an 
absolute loss of energy only a very small one. The 
law of the conservation of energy may be the expression 
that this loss is a minimum. 

This objection is not essential to the line of argument 
pursued above with regard to the conservation of energy. 
It forms no necessary part of the line of thought we are 
pursuing. It merely tends to show that the law of the 
conservation of energy is no axiom which we cannot 
suppose not true. The real conclusion to which this 
part of our line of thought tends is that the conserva- 
tion of energy is a purely formal law. 


ii4 Level. 


THE most apparently simple movements are those 
which we see taking place on the surface of the earth, 
connected with the agency which we call gravitation. 
We see the rivers flowing from a higher to a lower level, 
rocks when loosened from a mountain side rolling 
down, rain falling, and many minor changes of this sort. 

But there are many actions besides these. For in- 
stance, suppose before us a spring coiled up. When it 
unwinds it "exerts force," it transmits movement. In 
its first state it is like a stone at the top of a mountain. 
In its second state it is like a stone which has fallen to 
the bottom of the mountain. It had a power of move- 
ment and of communicating movement, now it has lost 
that power. 

Again, the powder in a gun when it explodes expands 
and imparts movement to the shot. When the gun has 
been fired off the powder enters a different state. Before, 
the chemical affinities of its constituents were in a state 
of tension, now that it is fired off, they have formed 
fresh combinations. The power of transmitting move- 
ment has been lost by that which was the powder. It 
is like a portion of water at the top of a fall of water. 
If it remains at the top it has at any time the power of 
producing a shock, and of effecting, say, the movement 
of a water-wheel under it. But if it falls it has exerted 
and lost that power. 

The difference of level associated with gravity is 
familiar to us. But we have no right, other than our 
own familiarity with it, to look on gravity as less in 
need of explanation than any other phenomenon of the 
external world. Newton did not suppose that there 
was any force inherent in matter which attracted other 

Level. 115 

matter inversely as the square of the distance. He 
showed that a great many astronomical facts were 
capable of being explained and calculated on this 
hypothesis. He left the explanation of how it is that 
matter gravitates unsolved, and it remains unsolved to 
the present day. 

But gravitation affords us a useful term " Level." 

Let us agree to call the following on a high level a 
stone at the top of a precipice, a wound-up spring, 
oxygen and hydrogen mixed in the proportion to form 
water. Let us call the following at a low level the 
stone at the foot of the precipice, a spring straightened 
so far as it tends to straighten, oxygen and hydrogen 
united in the form of water. 

In passing from their first state to their last all these 
have manifested a power of movement and of communi- 
cating movement. They have now relatively to their 
former state lost that power. 

Difference of level in this general sense is the most 
universal distinction of matter. 

No motion takes place unless matter passes from a 
higher to a lower level. 

The universal cause of motion is that which produces 
this difference of " level " in the general sense. 

If there were no difference of level the state of things 
in nature would be as if one spring in order to unwind 
had to wind up an exactly equal spring of the same 
amount ; as if a stone falling from a height had to raise 
an exactly equal stone to the same height from which it 
fell. Under such conditions of things no motion would 
begin. In such a state of things all nature would be 
like the inhabitants of the valley when the king bore 
no pain, for no course would be preferable to any other 

What is the cause of the " Difference of Level ? '' 

n 6 Level. 

Whenever matter passes from a higher to a lower level 
some of the energy which is given out passes away in 
the form of heat. This passing away of some of the 
energy into the form of heat is an invariable accompani- 
ment of the transition from a higher to a lower level. 
Is it the cause of the difference of level ? 

In the valley the king by bearing some pain made 
action worth while. Is there any indication in nature of 
the production of a lower level which makes the course 
of things run on. 

It is certain that energy in every action passes off into 
the form of heat, and unless it is through the power of 
the finer particles of matter to absorb the energy, it is 
difficult to see how any action can take place. 

As with the other lines of thought, this line also ter- 
minates with a possibility. Nothing has been proved, 
but a place has been provided. 

In the first part of this paper a possible mode of 
action was exhibited in the imaginary relations of a world 
subject to certain laws of pleasure and pain. 

In the second part it has been shown that something 
is wanting in our conception of the natural processes. 
There is room for a central idea. No scientific doctrines 
properly understood would clash with one properly 

Can the mode of action exhibited in terms of sensation 
in the fictitious world be applied to the case of the world 
of force and matter ? 

Before passing on, however, it is worth while to exa- 
mine a little more closely into what is meant by the 
expression so often used : " Passing off into the form of 

The modes in which energy passes off into the form of 
heat are in general those modes by which movement is 
brought to a standstill such as friction. And we are apt 

Heat. \ 1 7 

to think motion the primary fact, the cessation of motion 
a secondary and disagreeable fact. But both are equally 
existent phenomena, and the convenience to ourselves is 
not to mislead us as to their relative importance. 

But what is this passing off of energy into the form 
of heat ? The phrase is unsatisfactory, for we are told 
by science almost in the same breath that heat is the 
motion, the mechanical motion, of the particles of matter. 
So the statement resolves itself into this. Only when 
some of the motion passes off into the form of motion 
of the smaller particles of matter does motion take place 
in larger masses. 

As a corollary it follows that at some date, however 
distant, all the motion of masses will have passed away 
into the form of motion of smaller masses. 

It may be urged that when the larger masses move, 
the smaller particles also move. This is true ; but 
motion in this sense is used to denote change of position 
amongst the smaller particles with regard to one another. 
The particles in a flying cannon-ball are relatively still 
with regard to one another as far as the motion of the 
cannon-ball as a whole is concerned. 

We thus arrive at the following principle : The con- 
dition of the motion of masses taking place is that some 
of the motion passes off into the motion of the smaller 

But if the motion of the smaller particles is just the 
same as that of the larger portions, we are obviously not 
at the end. The very same principle just applied must 
be applied again. 

These motions of the small particles of matter cannot 
take place unless some of their movement is transmitted 
and passed on, and transformed into the motion of still 
finer particles of matter. 

But here obviously we are brought to the beginning of 

1 1 8 Ultimate Medium. 

an infinite series. An infinite series passing from finer 
matter to still finer matter, and so on endlessly. 

The assumption by which we are led to this endless 
series of transmissions must be clearly apprehended. 
We take the law that the motion of masses only takes 
place when some of the motion passes off into the 
motion of the finer particles of matter, and we assume 
that it holds always. 

In a lever there is a fixed point, the fulcrum, which 
supports it, and the power raises the weight ; but the 
weight may be fixed, and then the fulcrum can be lifted 
by the power. So we obtained this law from the con- 
sideration of material relations ; and now we suppose 
this law to be the fixed point, and shift our notions 
of material relations. 

Thus we are landed on an endless series. Before pro- 
ceeding, however, to inquire what the significance of this 
endless series may be, let us assume an end to it. Let us 
assume that we come at last to a final transmission. Let 
us assume that the energy is transmitted to the ultimate 
particles of matter. 

Or, if we have gone beyond matter, let us suppose an 
ultimate medium which by its modifications builds up 
matter, and which is the last and ultimate substance. 

Let us suppose this ultimate medium absolutely to 
receive some of the energy. Let it absolutely receive 
and absorb some of the energy, and thereby give rise to 
the difference of level, to give the ultimate permission 
which sets all things going. 

What are the properties of this medium ? We obtain 
an indication of what they are when we examine the 
properties of the finer kinds of matter. Compared with 
the motions of masses, motions which affect the smaller 
particles of bodies are infinitely quick. Light and elec- 
tricity are actions affecting the smaller particles of 

Ultimate Medium. 119 

bodies, and by them distances are speedily traversed, 
which relatively to moving masses are very great. 

Now in point of speed of transmission the properties 
of this ultimate medium must be infinitely beyond those 
of luminiferous ether. 

To this ultimate medium all movements at any dis- 
tance from each other must be almost equally present at 
every part At whatever distance from one another two 
affections of this ultimate medium be supposed to take 
place, the effect of the one will travel to the place of 
action of the other instantaneously. 

Such a medium is a kind of visible symbol of the 
universe, being one system in which all motions should 
be co-determined. 

To make this clear, suppose a transformation of energy 
was produced in one part of space of an absorption of 
energy on the part of this ultimate medium, this trans- 
formation of energy would be produced by a medium in 
instantaneous contact with every other part of space, and 
the transformation of energy thus originated would har- 
monize with, and have reference to, the transformations 
of energy in every other part of space. 

There are two infinities the infinite of space extend- 
ing out each way, the infinite of the smaller and smaller 
divisions of matter. The ultimate medium we have sup- 
posed partakes of both infinities. It is infinite in extent, 
and infinitely fine in its particles. 

Now this medium by absorbing energy sets move- 
ments going. And that movements do not neutralize 
one another i.e., that movements in opposite directions 
do not mutually destroy one another has this result, that 
a given amount of this absorption produces the greatest 
possible amount of motion. If motion came to a rest 
in any other way, more of this absorption by the ultimate 
medium would be needed. Hence, by a given amount 

I2O Infinite Series. 

of absorption in the ultimate medium the greatest pos- 
sible amount of motion is produced. That is, the 
absorption of motion into the ultimate medium is a 
minimum, and the law of the conservation of energy is 
the expression of this being a minimum. 

But here again a further remark is called for. We start 
by assuming energy to be an absolute existence. But 
why not assume this action on the part of the ultimate 
medium to be the real action, and consider the pheno- 
mena of motion and energy as the mode of its action. 

What this action of the ultimate medium may be 
needs examination. All that we can say at present is 
that relatively to that which we call energy, the action 
of this medium is that of being acted on. 


IN the preceding, however, it must be remembered that 
this conception of an ultimate medium was merely a 
supposition to enable us to see and roughly map out the 
relations of the things we are investigating. Where we 
were really landed was in an infinite series we were 
brought logically to the conception of an infinite series 
of media, one behind the other. 

What does an infinite series indicate ? 

Let us turn to a region of thought where infinite series 
are familiar objects, and we can learn about them. 

In algebra infinite series are common. Thus take 

series I f- - and so on for ever. This is the attempt 
2 4 

in algebra to represent a trigonometrical idea. In trigo- 
nometry it is expressed as cos. x. But in algebra it 
needs this infinite series. 

Infinite Series. 121 

In algebra infinite series occur when the object which 
it is wanted to represent in algebraical terms cannot be 
grasped by algebra. When there is no single term 01 
set of them in algebra which will serve, the object is 
represented by means of an infinite series. Thus we 
may say that in any calculus, when the object to be 
treated of cannot be expressed in the terms of the cal- 
culus, it is represented by means of an infinite series. 

Now, dealing with material considerations, going on 
in the calculus of matter, we have come to an infinite 
series. This indicates that we have gone as far as the 
material calculus will carry us. We have now to bring 
in an idea from a different quarter if we will simplify 
our expression. 

It may well be that within our experience there is 
nothing which will serve. But let us suppose that that 
which in material terms we represent as an infinite series 
is a will a will in contact with all existence, as shown 
by the properties it had when we conceived it as an ulti- 
mate medium. For, regarding it as an ultimate sub- 
stance, we found that it would be affected by pulsations 
infinitely quicker than light and electricity ; considered as 
a substance, it was such that distance to it tended to be 
annihilated. Hence as a will we must say of it that to 
it all that is is present a will which by a fiat that to our 
notions is being acted on rather than acting, accepting 
pain rather than taking pleasure, sets the course of the 
world in motion, which holds all in one system, which 
creates all activities. For although we apprehend this 
will relatively to the appearances which we suppose we 
know, mechanical energy and feeling, still we see that 
both are caused by it, and that the sum of both is 
nothing, save for that which this will is in them. 

Is there any other way of apprehending this will than 
through the external world ? 

122 Recapitulation. 

We have two apprehensions of nature one of ex- 
ternal things, the other of our own wills. 

Does this will not exist in those who are true per- 
sonalities, and not mere pleasure-led creatures ? have 
they not some of this power, the power of accepting, 
suffering, of determining absolutely what shall be? a 
creative power which, given to each who possesses it, 
makes him a true personality, distinct, and not to be 
merged in any other a power which determines the 
chain of mechanical actions, of material sequences 
which creates it in the very same way in which it seems 
to be coming to an end by that which, represented in 
material terms, is the absorption of energy into an ulti- 
mate medium ; which, represented in terms of sensation, 
is suffering ; but which in itself is absolute being, though 
only to be known by us as a negation of negations. 


IN conclusion let us remark that we have supposed two 
different worlds one of sensation in the first part, one 
of motion in the second part. And these have been 
treated as distinct from one another. And especially in 
the first part, by this avoidance of questions of move- 
ment, an appearance of artificiality was produced, and 
occasionally inconsistencies, for sometimes sensations 
were treated as independent of actions, sometimes as 
connected with them. But it remains to be decided if 
these inconsistencies are in themselves permanent, or 
whether, when we remove the artificial separation, and 
let the world of sensation and the world of motion 
coalesce, the inconsistencies will not disappear, thereby 
showing that their origin was merely in the treatment, 

Recapitulation. 123 

not in the fact ; that they came from the particular plan 
adopted of writing about the subject and are not in- 
herent in the arguments themselves. 

The king in the first part was supposed to have all the 
material problems of existence solved. There was a com- 
plete mechanism of nature. He took up the problem of 
the sentient life. But this problem can only artificially 
be separated from that of the material world. The gap 
between our sensations and matter can never be bridged, 
because they are really identical. 

Let us then allow this separation to fall aside. Let 
us suppose the king to have all the reins of power in his 
own hands. Let us moreover suppose that he imparts 
his rays to the inhabitants so that they have each a por- 
tion of his power. And let us suppose that the inhabi- 
tants have arrived at a state of knowledge about their 
external world corresponding to that which we have 
about the world which we know. 

Let us listen to a conversation between two of them. 

A. The energy of the whole state of things is running 

B. How do you prove that ? 

A. Whenever any motion of masses takes place a 
certain portion of the energy passes irrecoverably into- 
the form of heat, and it is not possible to make so large 
a movement with those same masses as before, do all 
that is possible to obtain the energy back again from 
the heat into which it has passed. 

B. Well, what about the heat ? Energy in the form 
of the motions of the masses passes off into the energy 
of heat. But what is heat ? 

A. It is the motion of the finer particles of matter. 

B. Well, I would put forward this proposal. We 
have by observation got hold of a certain principle that 
where any movement takes place some of the energy 

124 Recapitulation. 

goes in working on the finer particles of matter. Let us 
now take this principle as a universal one of motion, 
and apply it to the motions of the finer particles of 
matter themselves, which are simply movements of the 
same kind as the movements of the larger ones. This 
principle would show that these movements are only 
possible inasmuch as they hand over a portion of their 
energy to work on still finer matter. 

A. Then you would have to go on to still finer matter. 

B. Yes, and so on and on ; but to fix our thoughts, 
suppose there is an ultimate fine matter which is the last 
worked on. Now I say that we may either suppose that 
this is being gradually worked on and all the energy is 
dissipating, or else we may put it in this way. When 
we regard so much energy we are apt to think that it is 
the cause of the next manifestation in which it shows 
itself. But this is really an assumption. Energy is a 
purely formal conception, and all that we do is to trace 
in the actions that go on a certain formal correspondence, 
which we express by saying that the energy is constant. 

A. But I feel my own energy. 

B. Allow me to put your feeling to one side. If we 
take then the conservation of energy to be merely a 
formal principle, may we not look for the cause of the 
movements in the invariable accompaniment of them, 
namely, in the fact that a certain portion of the energy 
is expended irrevocably on the finer portions of matter. 
If now we take this ultimate medium which suffers the 
expenditure of energy on it, may we not look on it as 
the cause, and the setter in action of all the movements 
that there are. By its submitting to be acted on in the 
way in which it does submit, it determines all the actions 
that go on. For what is all else than a great vibration, a 
swinging to and fro. When we count it as energy, we 
by reckoning it in a particular manner make it seem to 

Recapitulation. 125 

be indestructible, but that the energy should be inde- 
structible would be a consequence from the supposition 
which we could very well make, that to produce a given 
series of effects the submitting to be worked on of this 
ultimate medium must be a minimum. If it were a 
minimum no movements could neutralize one another 
when once set going, for if they did there would be a 
waste of the submission of this ultimate medium. 

A. But what do you suppose this ultimate medium 
would be? 

B. That I cannot tell, but we seem to have indications. 
For the more fine the matter which we investigate, the 
more its actions seem to annihilate distance : light and 
electricity produce their effects with far greater rapidity 
than do the movements of masses. We might suppose 
that to this ultimate matter all parts were present in 
their effects, so that anything emanating from the ulti- 
mate matter would have the appearance of a system 
comprehending everything. 

A. But you have not got any evidence of an ultimate 

B. No, all that we can think of is an endless series of 
finer and and finer matter. But is that not an indication 
rather, not that the direction of our thoughts is false, but 
that there are other characteristics of this ultimate, so 
that when looked at under the form of matter it can 
only be expressed as an infinite series. 

Let us omit the considerations brought forward in the 
preceding conversation and examine more closely the 
philosophy of the inhabitants of the valley in so far as it 
corresponds with ours. 

They laid great stress on a notion of vis viva, or what 
we should term energy, but said it was gradually passing 
away from the form of movements of large bodies to 
that of movements of small bodies. So that in the 

1 26 Recapitulation. 

course of time the whole valley would consist of nothing 
but an evenly extended mass of matter moving only in its 
small particles and this motion of the small particles' 
they called heat. Now they had very clearly arrived 
at the conviction that with every mechanical motion 
there was a certain transference of vis viva to the 
smaller particles of matter, so that it did not appear 
again as mechanical motion. But they did not accept 
this as a principle to work by. They did not consider 
that the motions of the smaller particles of matter were 
just the same as those of the larger masses. They did 
not see that if a condition held universally for the move- 
ments of the visible world, it must also hold for the 
smaller motions which they experienced as heat. So 
the conclusion which they should logically have come to 
that there was a transference of vis viva on and on was 
not held. But the step was a very little one for them to 
take from regarding an invariable condition as always 
there to regarding it as a cause. For the causes they 
assigned were all purely formal relations, and only got 
to assume an appearance of effective causes by familiarity 
with them, and a throwing over them of that feeling of 
effectiveness which they derived from the contact which 
they had with the king. 

They might have reasoned. This universal condition 
of anything happening must be the cause. Energy goes 
from a higher to a lower level. That which causes the 
difference of level is the cause, and the cause of the dif- 
ference of level must be that which invariably accom- 
panies such a transference of energy from a higher to a 
lower level. Now this invariable condition is the passing 
of a portion of the energy into the form of motions of 
the finer parts of matter. Hence there is an apparently 
endless series. But to realize the matter, suppose an 
ultimate medium, suppose there is a kind of matter of 

Recapitulation. 127 

infinite fineness distributed everywhere which let itself 
be worked on, and so determines differences and wakens 
the sleeping world. What are the qualities of this fine 
matter ? We see them in the properties of the finer 
kind of matter which we know, such as light, electricity. 
The property of the finer kind of matter is in general 
that it tends to bring distant places together, so that a 
change in one part is rapidly communicated to every 
other part. If they followed this indication they would 
have supposed that the ultimate fine matter was of such 
a nature as to make all parts of the valley as one, so that 
there was no distance, and any determination of a differ- 
ence of level on the part of this ultimate matter would 
have reference to all the conditions everywhere. It 
would be in immediate contact with every part, so that 
anything springing therefrom would present the appear- 
ance of a system having regard to the whole. Now if 
they had imagined such an ultimate medium doing that 
which to them would seem bearing rather than exerting 
force, suffering rather than acting, they would not have 
been far from a true conception of the king who directed 
them all. For he himself by reason of his very omni- 
presence could not be seen by them. There was 
nothing for them to distinguish him by. But they could 
have discovered somewhat of the means by which he 
acted on them, which can only be described from the 
appearances they present to the creatures whom the 
king calls into life. 

But of truth they would have had another and perhaps 
a truer apprehension of the king in a different way. For 
when he acted on them so that they took one course 
rather than another, it was his action in themselves that 
they felt. If they were mere pleasure-led creatures then 
they were shaped outwardly, but if in their inner souls 
he acted and through them suffered, then they were true 

128 Recapitulation. 

personalities conscious of being true selves, the onen^. 
of all of them lying in the king, but each spontaneous in 
himself and absolute will, not to be merged in any other. 
Thus they had two modes of access to the king, one 
through their own selves where he had made them exist, 
one through the outer world. And in the outer world it 
was but a direction in which they could look. They 
could never behold the personality of the king, but only 
an infinite series of different kinds of matter, one sup- 
porting the other as it were and underlying it, but doing 
more also than this, for in proportion as they considered 
the kinds of matter that lay deeper they found that distant 
became near, absent, present, that time gave no longer 
such distinctions, but from the phenomenal side they 
seemed by a gradual diminution of the limitations of 
experience to arrive at an external presentation of that 
absolute which exists in the fulness of things, which they 
knew more immediately in themselves when they truly 


|N the next two or three of these papers certain 
questions connected with the subject of a 
space higher than our own will be treated. 
It is well, therefore, first to recede and to 
form definite conceptions about a world of plane space, 
about a world in which the beings can only move in two 
independent directions. Then, proceeding thence to our 
o\vn world, we may gain the means of passing on to a 
higher world. And I should have wished to be able to 
refer the reader altogether to that ingenious work, " Flat- 
land." But on turning over its pages again, I find that 
the author has used his rare talent for a purpose foreign 
to the intent of our work. For evidently the physical 
conditions of life on the plane have not been his main 
object. He has used them as a setting wherein to place 
his satire and his lessons. But we wish, in the first 
place, to know the physical facts. 

With this aim it is necessary to form a clear idea of 
what matter would be in a world of two dimensions, and 
the following illustration is a convenient one. 

Place on the smooth surface of a table a half-crown 
piece, and suppose it to slide on the table perfectly 
freely. Imagine it to exercise an attractive force along 
the surface of the table in all directions round itself. 
By it and near it place a sixpence, and let the sixpence 
also slide freely on the table. It will, however, not be 


T 30 Introduction. 

so free to move equally in all directions as the half- 
crown was, for it will be attracted by the half-crown. It 
will slip over the surface of the table under the influence 
of this supposed force, and will come into contact with 
the half-crown. Now if we suppose that both the half- 
crown and the sixpence are very thin, that they are both 
of them only the thickness of the ultimate particles of 
matter, then we shall have a representation of what 
material bodies will be in a plane world. 

We must suppose that the particles cannot lift them- 
selves or be lifted up from the plane so as to lie upon 
each other. Under no circumstances can they quit the 
surface of the plane. 

Moreover, at no point must the particles adhere to the 
plane, nor must there be any friction impeding their 
movements over it. The only purpose which the sup- 
port serves is to keep them on the same level surface 
and to convey influences from one particle to another. 
The gravity which we know, and which acts at right 
angles to the table on which the coins rest, will not 
have any effect on the particles in their motions on the 
plane, but will simply keep them to the plane. Any 
force of attraction which concerns their motions proceeds 
from one particle to another. Thus, conceive the half- 
crown to be a very large disk of matter, and the six- 
pence to be a sentient being. This being would feel a 
force of attraction towards the centre of the half-crown,, 
and this force of attraction would keep him to the rim 
of the half-crown. If he weighed anything it would be 
by balancing it with his weight against the force which 
tended to pull it to the centre of the half-crown. He 
would not feel the gravity which keeps him against the 
surface of the table ; he would not know that there was 
a hard, smooth surface on which he rested. He would 
always have been in contact with it, and so he could not 

Introduction. 131 

tell what it would be like to be free from it. He would 
have no contrast whereby to apprehend its effect on him. 
Moreover, he would only know of movements in di- 
rections along the plane. He would not conceive that 
such a thing was possible as movement in another 
direction than to and fro, hither and thither on the 
plane. It is difficult to suppose that a being would be 
supported on one side by a plane, and not be in contact 
with anything on the other side, even atmosphere. Yet 
if we suppose a being of real matter free to move on the 
plane, this is what must be conceived. If the sixpence is 
conceived as such a being, it must receive its impressions 
through its rim. The rim represents its skin. 

And if it be supposed to be surrounded by air for its 
respiration, this air must not be able, any more than the 
particles of solid matter, to rise away from the plane. 
The plane being must be conceived to have a different 
air to that which we know. The particles of its air, 
however free to move amongst themselves, must not 
have the power of moving away from the surface of the 
plane, as if so they would be able to pass to the interior 
of the body without passing through the skin. Any 
passage leading to the interior of the body would have 
to terminate in an opening in the rim, otherwise it would 
be completely shut up from the exterior. 

Xow it is obvious that if the table is struck so that it 
quivers, this movement will be communicated to the 
coins lying on it. Either the coins as a whole will 
move, or their particles will be disturbed. 

Again, if we suppose there to be some particles loosely 
cohering together, lying on a smooth sheet of iron, it is 
evident that the quivering and jostling of the iron, if it is 
struck, would have an effect on the particles, and may 
cause the breaking up of the thin masses in which the 
particles cohere. Thus, if the material of which the 


sheet is composed be very dense and rigid, compared 
to the substances lying on it, they may undergo many 
alterations, being broken up and coming together again 
while the supporting matter which bears them all uf 
simply moves and vibrates. 

It is evident that just as the particles are affected by 






Diagram I. 

the vibration and shaking of the sheet of metal on which 
we suppose them, so they might in turn possibly affect the 
sheet of metal and cause vibrations and shakings in it. 
These shakings and vibrations would go forth from a 
particle which excited them in every direction along 
the sheet. They would not pass out into the air, except 

Introduction. 133 

secondarily and in a very minute degree. The shake 
would be transmitted in the sheet. And the effect on 
neighbouring particles would be great, on more distant 
particles it would be less, and on those at a great dis- 
tance barely perceptible. 

The following is a good plan for obtaining in a defi- 
nite way the feeling of what existence in a plane would 
be like ; it enables us to realize the conditions in such 
a way as to lay the basis for subsequent thought. 

Let the reader take a sheet of note-paper and hold it 
before himself edgewise, so that he sees it with one eye 
as a single line. And let him hold it so that this line 
runs downwards from his eyebrows to his mouth, as 
shown in Diagram I. Now on this sheet of paper, on 
one side of it, let a straight line be drawn running across 
it, away from the observer. Suppose all below this line 
to be a thin layer of particles which, keeping compactly 
together, form a solid sheet of particles, every one of 
which touches the paper. This would be the solid earth 
to a being in the plane world. 

Let the surface of the paper above this be covered 
by a layer of particles which move freely amongst each 
other, but which do not rise from the surface of the 
paper. These particles form the air of such a world. 

On the surface of the earth draw a line standing up- 
right. Let this line represent a man. Another line will 
represent a wall which the man could not pass except 
by getting over it. 

It will be found that the objects on the paper are felt 
to be subject to the action of gravity. The question will 
occur, Why will not this thin layer of particles slip off 
the paper ? 

Now, the sense of gravity must not be got rid of, but 
it must be connected with the matter in the sheet of 

134 Introduction. 

Suppose, then, that the sheet were to grow bigger and 
bigger till it filled out reaching through the whole world 
and cutting the globe in two. Then let all the earth be 
removed except a thin layer on one side of this enlarged 
sheet of paper. This thin layer will be the only portion 
of matter left. And such a thin layer will represent a 
plane world. The force of gravity must be conceived as 
remaining, but as coming from a large and thin disk. 

Now to keep this thin layer on the paper it would be 
necessary to have some force acting sideways, so as to 
keep the particles to the paper. 

And the paper itself may be conceived to exercise 
such a force : it is many particles thick, while the thin 
layer of matter is only one particle thick, and thus it 
will keep the layer of matter, which covers one side of 
it, in its place by virtue of its own attraction. 

We suppose that the paper exerts an attractive force 
which keeps the thin layer of matter to it. This attrac- 
tive force is not felt by the sentient beings on the paper, 
nor does it influence the movements of the particles of 
matter amongst themselves. We also suppose another 
attractive force proceed ing from particle to particle 
of the matter on the plane. This would be felt by the 
beings and produce movements of matter. 

Thus the conception of a plane world necessarily 
involves that of something on which it is. 

HERE the sun's rays grazing the earth in 
January pass off and merge into darkness lies 
a strange world. 

Tis a vast bubble blown in a substance 
something like glass, but harder far and untransparent. 

And just as a bubble blown by us consists of a dis- 
tended film, so this bubble, vast beyond comparison, 
consists of a film distended and coherent. 

On its surface in the course of ages has fallen a thin 
layer of space dust, and so smooth is this surface that the 
dust slips over it to and fro and forms densities and 
clusters as its own attractions and movements determine. 

The dust is kept on the polished surface by the 
attraction of the vast film ; but, except for that, it moves 
on it freely in every direction. 

And here and there are condensations wherein have 
fallen together numbers of these floating masses, and 
where the dust condensing for ages has formed vast disks. 

And these disks are glowing hot yet no light comes 
from them into our universe. 

For this world lies beyond the aether far beyond. And 
however hot or glowing the masses are, if there is no 
medium to transmit the vibrations of heat the influence 
cannot travel. 

Thus the only directions in which the heat can travel 

136 A Plane World. 

are on the film. From each of these glowing disks the 
luminous influence streams forth carried by the vibrations 
of the film which supports everything. For the heat and 
intense agitation of these glowing disks shakes and dis- 
turbs the bubble, and just as a thin soap bubble quivers 
and shakes, so this film quivers and shakes. And so 
elastic is it, and so rigid, that it carries the light and heat 
to all surrounding regions. Yet so vast is the bubble, so 
tremendous in its dimensions, that the agitation from 
these glowing disks travels almost in straight lines, till, 
spreading out on every side, it merges into darkness 
like the ripples in the centre of a vast calm lake gradually 
become indistinguishable. 

And round these central orbs of fire for orbs of fire 
they are, though they only transmit their fire along the 
film of the bubble round these orbs pass in due order 
and succession other disks, which, cold or warm, have not 
that energy of light and heat which the central orbs 

These disks, though large, are so immeasurably small 
compared with the vast surface of the all-supporting 
bubble, that their movements seem to lie on a plane flat 
surface ; the curving of the film on which they rest is so 
slight compared to their magnitude, that they sail round 
and round their central fires as on a perfect level 

And one of these orbs is fitted by nature to be the 
habitation and home of living beings. For it is neither 
so hot as it was for long ages after it had condensed from 
the film of dust wherefrom all orbs are made, nor has it 
so cooled down as to render life unsupportable. 

And, moreover, it is full of vast crevices and channels, 
for in many places the interior in cooling after the rim 
had set from its molten condition has left long caverns 
and passages, not only in one layer, but in many. 

A Plane World. 137 

And on the rim and in these passages and caverns 
live the inhabitants of whom I speak. 

They do not rise from the surface of the film, but as 
all matter lies on the smooth surface but one particle 
deep, so their bodies formed out of matter lie, as we 
should say, on this smooth surface. 

Yet of this they know nothing. They say that they 
stand and walk. 

For this orb has an attractive force. 

By that very same impulse of coming together whereby 
it gathered its particles out of the dust on the bubble, 
by that very same force it draws towards its centre all 

Diagram II. " Two beings walking round." 

that is near it or on it. Thus " up" is to these inhabi- 
tants a movement from the centre of the disk on the rim 
of which they live and away from it. " Down" is a move- 
ment from the rim towards the centre. The thin layer 
which forms the mass of the disk is their solid matter. 
They are not able even in thought to rise away from the 
surface of the bubble, and look from space upon their 
mode of existence. They ever pass to and fro upon a 
line, upon a rim ; and no two can walk except after one 
another. If you look at the rude picture you will see 
that the two beings represented by two triangles cannot 
pass one another if they are unable to lift themselves up 
from lying on the surface of the paper. The surface of 

138 A Plane World. 

the paper represents the surface of the bubble, and sliding 
freely on it, but unable to lift up from it, are tenuous 
shapes that are the inhabitants, and that thin layer of 
particles that is to them solid matter. 

B __ D Now were it not 

,...,-. *-^ ^ lv ::-.. for the fact that the 

-'--" E orb is reft into these 
c v chasms and pas- 

Diagram III. A section of the film 01 the bubble ,, , 

showing a disk BD lying on it, and a creature Sages,tne Only mOVC- 

AB on the rim of the disk. CE is a section ment t h at these 
of the film, BD is a section of the disk, AB is 

a section of the creature. The thickness is beings would have 
enormously magnified and also the height AB , . . r 

of the creature compared with the diameter WOUld DC OI pass- 

BDofthedisk. The attraction which A B feels : no - t-nnnrl anH rrmnrl 

keeps him to BD ; both AB and BD, the being m ^ rC 

and the disk, slide freely on the film CE on the rim of their 
without knowing of its existence. , , 

Many words that we have, to them could bear no 
meaning. Thus " right and left " is to them unknown. 
For consider their faces bent in one direction along the 
rim. In following this direction, they go forward, in 
retracting from it they go backward. If they go away 
from the centre they go up, towards the centre is down. 
And by no means can they turn, raising themselves from 
the surface \vhereon they are. They do not even know 
that they have two sides ; their movements, thoughts, and 
imaginations are all confined to that surface on which 
they are. This they call their space, their universe; 
nor does aught that lies beyond it, towards the interior 
of the bubble or away from it, directed outwards, come 
into their thoughts, even as an imaginary possibility of 

Life is extremely limited on such a world. To take a 
single instance, in order for two beings to pass each other, 
a complicated arrangement is necessary, shown in Dia- 
gram IV. 

At intervals along- the rim recesses and chambers are 

A Plane World. 


constructed. Near the openings of these chambers lay 

movable plates or rods. When two beings wish to pass, 

one of them descends into the recess; the other one 

pushes the rod 

so as to form a 

bridge over the 

opening, walks 

across it, and 

then removes 

the plate so 

Diagram IV. Two beings passing. 

that the one who has descended can get up and go on 
his way. 

If by any chance, while a being is in the recess, the 
plate or rod which acts as a bridge gets fixed, he is in a 
dangerous predicament. For suppose a being confined 
as shown. If he, suffering from want of air, cuts through 
the roof at AB, the whole part to the right of AB comes 
tumbling down. For its only support is severed when 
AB is cut through. It is impossible to make a hole 
which is not the whole width of matter as it lies on the 

surface. And with 
regard to this all con- 
structions have to be 
made. There cannot 
be two openings in a 
wall of a house, un- 
less when the one is 
open the other is so 
fashioned as closing 
, to act as a rigid sup- 
port to the wall, 
which now depends for its upholding entirely on it. 

Thus, in the diagram, the house is held up entirely by 
the side opposite to the doorway EF, which is now open. 
The roof is supported by the side CD. If an opening 

Diagram V. A house. 

140 A Plane World. 

AB be made in the wall CD bsfore the doorway EF is 
closed, the roof will fall in. So, in order to pass through 
the house, EF must be firmly shut up before AB is 
opened. The houses are always built in the interior 
passages so as to leave the rim of the disk free for 

And there are many things to be said of the inhabitants 
on this disk with respect to their social and political life. 
It is hardly necessary for me to put down much about it 
here, for any one by using the method of the historian 
Buckle, and deducing the character of a people from 
their geographical influences and physical surroundings, 
could declare what the main features of their life and 
history must be. 

But one or two remarks may be made here. First of 
all they are characterized by what I may venture to call 
a crude kind of polarity. 

In dwellers in our world this polarity, which shows 
itself amongst other ways in the distinction of sexes, is 
tempered and modified. 

In every man there is something of a woman, and in 
every woman there are some of the best qualities of a 

But in the world of which we speak there is no phy- 
sical possibility for such interfusion. In a linear exist- 
ence there would be no consciousness of polarity. It 
makes its appearance first in the plane, and in a hard 
and unmitigated form. 

It is impossible to do otherwise than caricature these 
beings when we write of them thus in brief. So let us 
accept the matter frankly, and, without scruple, look at 
them in the broadest possible manner. 

If the reader will cut out the triangles in the corners 
of the two next pages he will obtain four plane beings, 
two of which are men, two of which are women. The 





Diagram VI. 


Diagram V1L 

A Plane World. 145 

lines down which the cutting is to be made are marked 
with a black line. Now having cut out two men, whom 
we will call Homo and Vir, draw a line on a piece of 
paper to represent the rim of the world on which they 
stand, and, remembering that they cannot slide over each 
other, move them about. It must be remembered that 
the figures cannot leave the plane on which they are put. 
They must not be turned over. The only way in which 
they can pass each other is by one climbing over the 
other's head. They can go forwards or backwards. 
Much can be noticed from an inspection of these figures. 
Of course it is only symbolical in the rudest way, but in 
their whole life the facts which can be noticed in these 
simple figures are built up and organized into compli- 
cated arrangements. 

It is evident that the sharp point of one man is always 
running into another man's sensitive or soft edge. Each 
man is in continual apprehension of every other man : 
not only does each fear each, but their sensitive edges 
those on which they are receptive of all except the 
roughest impressions are turned away from each other. 

On the sensitive edge is the face and all the means of 
expression of feeling. The other edge is covered with 
a horny thickening of the skin, which at the sharp point 
becomes very dense and as hard as iron. It will be 
evident, on moving the figures about that no two men 
could naturally come face to face with each other. 

In this land no such thing as friendship or familiar 
intercourse between man and man is possible. The 
very name of it is ridiculous to them. For the only 
way in which one man can turn his sensitive edge to 
another man is if one of them will consent to stand on 
his head. Fathers hold their male children in this way 
-when little, but the first symptom of manhood is con- 
nected with a resentment against this treatment. 

146 A Plane World. 

If now two women, Mulier and Femina, be looked at, 
the same relation will be seen to hold good between 
them. By their nature they are predisposed, by accident, 
to injure one another, and their impressionable sides are, 
by the very conditions of their being, turned away from 
each other. 

If now, however, Homo and Mulier be placed together, 
a very different relationship manifests itself. They can- 
not injure one another, and each is framed for the most 
delightful converse with the other. Nothing can be 
more secure from the outside world than a pair of ap- 
proximately the same height ; each protects the sensitive 
edge of each, and their armoured edges and means of 
offence are turned against all comers, either in one direc- 
tion or the other. But, if the pair, through a mutual 
misunderstanding, happen to be disadjusted, and, their 
feet on the rim, turn their sharpnesses against one another, 
they are absolutely exposed to the harms and arrows of 
the world. 

Still, even in this case they cannot wound one another 
a happy immunity. 

In the annals of this race which I have by me I find a 
curious history, which, unintelligible for ages to them, 
admits by us of a simple explanation. 

It is said that two beings, the most ideally perfect 
Vir and Mulier, were once living in a state of most 
perfect happiness, when, owing to certain abstruse studies 
of the Mulier, she was suddenly, in all outward respects, 
turned irremediably into a man. Vir recognized her 
as the same true Mulier. But she occupied the same 
position with regard to him which any other man would. 
It was only by standing on his head that he could, with 
his sensitive edge, approach her sensitive edge. She 
refused to explain how it was, or impart her secret to 
any one, but she had, she said, undergone a great peril. 

A Plane World. 147 

She manifested a strange knowledge of the internal 
anatomy of the race, and most of their medical know- 
ledge dates from her. But no persuasion would induce 
her to reveal her secret ; all the privacy of existence 
would be gone, she said, if she revealed it. She 
was supposed to have acquired some magical know- 

This possession, however, did not make either of them 
happy, and one day, with fear, she said that she would 
either die or be restored to the outward semblance of 
her sex. 

She disappeared absolutely ; although she was sur- 
rounded by her friends, she absolutely vanished. And 
had it not been that some days afterwards, cutting 
through the solid rock for the purposes of some excava- 
tions, they accidentally came on a chasm, they would 
never have found her alive again. For she was found in 
a cavity in the living rock, warm and beautiful her old 
self again. 

Her secret died with her. 

From our point of view it is easy to see what had 
happened. If the figure Mulier be taken up and turned 
over it will be easy to see that, though still a woman, 
her configuration has become that of a man. To all 
intents and purposes she is a man. She is rendered 
incapable of that attitude which is the natural one 
between the men and women in this land, and the 
happy relationship between her and Vir is neces- 
sarily and entirely broken off. Move about as you 
will, keeping her figure turned thus on the plane, you 
will not be able to make her a fitting helpmate for her 
unfortunate Vir. She must have discovered the secret 
of raising herself off the surface, and by some accident 
been turned over. Perhaps she had used this new posi- 
tion to study anatomy for to an observer thus situated 

148 A Plant World. 

the interior of every body would lie perfectly open and 
in prosecuting her studies had overbalanced herself. 

I have only mentioned this anecdote, however, for the 
sake of a curious observation which was made at the 
time. It was found that when she was in this trans- 
formed condition she was absolutely without atmosphere. 
To explain : ordinarily, apart from anything she said or 
did, there was a kind of influence proceeding from her 
which made her presence agreeable to Vir. When she 
was turned over she lost this. Now the explanation of 
this is obvious. To these people light is the agitation 
of the surface of the bubble; transparent objects are 
those which do not hinder this agitation in its course. 
But most bodies and the physical frame of the inhabi- 
tants amongst them were not transparent, but stopped 
and reflected these agitations of the film, thus sending 
off from their outer edge those vibrations which excited 
sight in their fellows. But besides these vibrations of 
light there were finer ones still which were not damped or 
deflected by the outer edge of the body, but came 
through the greater part of their frame as if it was 
transparent. In the interior, however, of their organiza- 
tions there were certain regions which did arrest these 
subtler vibrations, and which had (as the eye of light) 
the power of appreciating them. In connection with 
these regions there were certain structures, extremely 
minute, which had the converse power of agitating the 
film, and so sending forth through the periphery of the 
body these same minute vibrations. These organs were 
not of any use, but they formed a sort of means of sym- 
pathetic communication between the inhabitants, acting 
in no very defined way, but certainly producing a sensa- 
tion of a vague kind. Now when Mulier was turned in 
the way described, the relation of her frame to the film 
of the bubble was disarranged, and it was no wonder 
that this " atmosphere " disappeared. 

A Plane World. 


In many respects the inhabitants of this world are far 
more advanced than we are, having a simpler problem 
how to deal with matter in one plane they have advanced 
more nearly to a complete knowledge of its properties. 
Yet great as their knowledge is, their performance is 
small. If you but reflect on one single fact, you will see 
how limited all their efforts must be. TJiey cannot fix 
tJie centre of a wheel, so that it rotates 
round an axis. For consider a wheel 
a small disk lying on their plane. 
The centre on every part of it, 
touches the surface of the bubble on j 
which all things slide freely. To fix 
this point they would have to drive 
down into the film a thing which 
they cannot do, and which they are 
far from even imagining. 

If they make an opening in the 
disk they can arrive at the centre of 
it. But then the rod of matter which 
they put in will prevent the disk 
from revolving. 

The nearest approach to a wheel with a fixed centre 
which they can attain is shown in Diagram VIII., a por- 
tion of a circular disk which oscillates about the smooth 
end of a rod built into the substance of the cut-away disk. 

DC s B A Their carts 

are shown in the 








figure. They are 
as the rod is pulled 
slides along 

simply rods placed on rollers: 

along, the rollers turn, and the rod 

just as a boat does on the rollers whereby sailors help 

themselves in hauling it up the beach. As soon as 

these rollers roll from under the rod, as it goes on in its 

150 A Plane World. 

forward motion, they have to be secured, and then lifted 
over the cart and put down in front. Thus there are to 
each cart a set of little disks or rollers, and, as the cart 
goes on, these rollers have to be lifted over the cart from 
the back to the front. 

There is no means by which this can be made a 
continuous action. Each roller has to be waited for, 
lifted separately, and carried over separately. And to 
put it down in front, the rope by which the cart is dragged 
along has to be unfastened and fastened up again. 

Looking at the Diagram IX. it will be seen that there 
is a hollow in the body of the cart. On the part A B 
the driver sits. In the hollow from B to C is put the 
load. The load cannot then slip out over the ends of 
the cart. There is nothing in the cart to prevent it from 
falling out sideways. 

But the contents, as the whole body of the cart, are 
kept to the smooth surface of the bubble, and are thus 
supported by it on the side remote from the reader's eye, 
and also are kept from rising away from this surface 
by the force of attraction exerted by the film. 

Thus the surface of the bubble and its attractive force 
supply the other two sides of the cart. 

But of these two sides, the beings are ignorant, and it 
seems to them perfectly natural that loads of any kind, 
even of fluids, should be kept securely in a cart with two 

The method by which the rope is fastened to the cart 

_ R is this : C is the body 

of the cart ; R is the 
rope ending in a 
wooden step B ; A is 

Diagram X. How a rope is fixed to a cart, an oblong piece of 

wood. When the rope has to be taken out, A is lifted out 
by its handle, B is slipped back and taken out of the recess 

A Plane World. 151 

in C, and then the rope is free from the cart. And in a 
similar way it is secured again. 

One very ordinary way of driving machinery with us 
is by shafting. A long rod is driven round and carries 
wheels at different places along its length. Now with 
these inhabitants it was impossible to do this, because 
the twisting motion round a rod could not be imparted 
without going out of the thin layer in which they were. 
Their methods of transmitting motion were by long rods, 
by a succession of short rods, by pendulums attached to 
one another, or finally by wheels which drove one another, 
but which were held by smooth sockets fitting round the 
rim far enough to steady them, but not so far as to 
hinder them from touching each other. 

As to their science, the best plan is to give a short 
account of its rise. 

They discovered that they were on a disk rotating 
round an inner centre, and also proceeding in a path 
round the source of light and heat. 

They found that they were held in their path by a 
force of attraction. But this attractive force was not 
with them as it is with us. With us, since the effect 
which any particle has on the surrounding particles 
spreads out in our space if the distance is doubled from 
a centre of attraction, the force it exercises becomes one- 
quarter of what it was when at the less distance. 

With them, however, when the distance doubled,. the 
force of attraction became only one-half of what it was 
.at the less distance. For the light, or attraction, or 
force of any kind emanating from a particle, only spreads 
along the film, and does not pass out into the space above 
or beneath. If they had been on a thick globe instead 
of a bubble, the laws of attraction would have been the 
same as with us. But the bubble on which they were 
was thin compared with the paths along which the radiant 

152 A Plane World. 

forces spread forth. And thus every force being kept 
to one plane diminished as the distance from the centre 
of its action. 1 

Now it was a great problem with them how the light 
came from the central orb. Their atmosphere, they 
knew, extended but a small distance above the surface of 
their disk. And it was quite incapable, moreover, of con- 
veying vibrations such as those of light and heat. 

By studying the nature of light they became convinced 
that to transmit it there must be a medium of extreme 
rigidity between them and the great source of light. 

It is easy enough to see that what they thought was a 
medium between them and their sun was in reality the 
rigid surface on which they rested. This elastic film 
vibrated in a direction transverse to the layer they 
called matter, and carried the particles of matter with it. 
But they, having no idea but that the surface on which 
they were was the whole of space, thought that space 
must be filled with a rigid medium. They found that 
the vibrations of the medium were at right angles to the 
direction in which a ray was propagated. But they did 
not conceive of a motion at right angles to their plane 
they thought it must be in their plane. 

It was a puzzle to them how their disk glided with so 
little friction through this medium. They concluded 
it was infinitely rare. They were still more puzzled 
when they had reason to believe it was an opaque sub- 
stance; and yet that it could be anything else than a 
medium which filled their space was inconceivable to 
them. They could never get rid of it from a vacuum, 
however perfect. Indeed we see that in producing a 
vacuum they merely cleaned the surface on which they 

In one respect it might have been advantageous if 
1 See Appendix. 

A Plan^ World. 153 

they had known, for, their law of attraction being what it 
was, their movement round their sun was not destined 
to go on for ever ; but they were gradually falling nearer 
and nearer. Now, if only they had made the attempt, 
they might by some means have got a hold on the sur- 
face on which they were, and, by means of a keel which 
tended to furrow it, have guided their world and them- 
selves in their path round their sun. Indeed, it is possible 
to imagine them navigating themselves whither they 
would through their universe that is, on the surface of 
their bubble. 

It was also unfortunate in another respect that they 
did not realize the fact of the supporting surface, for the 
feeling which they came to have of being suspended in 
space, absolutely isolated, was a very unsettling one, and 
tended to cause in them a certain lack of the feeling of 
solidarity with the rest of the universe. 

We have seen that their laws of mechanics were very 
different from ours. But they had after all an experi- 
ence of our mechanical principles, though in a curious 
way. In all motions of any magnitude moving bodies 
were confined to the surface of the plane. But where the 
small particles were concerned there was more liberty of 
motion. The small particles were free in their move- 
ment ; although they could not go more than a very small 
distance away from the film on which they rested, still 
they were capable of motion perpendicular to' it. Thus a 
long line of particles connected together could rotate as 
a whole, keeping straight like a twisting wire, and by 
means of many strings of particles thus connected, 
movements could be transmitted in a way which was 
totally unlike the mechanical movements to be seen in 
the case of large masses. 

This motion of rotation round an axis lying in the 
plane was to them what electricity is to us. It was quite 

154 -A Plane World. 

a mysterious force. But it was extremely useful in its 
applications. Having no idea of a rotation which in 
taking place went out of their surface, they could not 
conceive a reason for the results of such movements. 

It can easily be seen how many kinds of forces they 
could have. There was the spinning motion of the small 
particles on the surface. This they were aware of it 
produced many appearances, but it was not fitted for 
transmission across great distances, as each particle was 
apt to be hindered in its rotation by its neighbour. 
Sometimes, however, when conditions were favourable, 
many of these rotations were harmonious, and waves 
were produced in their matter resembling the waves in 
our ocean. 

There were only two other kinds of motion. One was 
an up and down vibration of the film carrying matter 
with it ; the other was the twisting of strings of particles 
which were rigidly connected together. The up and 
down motion of the film was to them light. Those 
kinds of matter which did not hinder this motion were 
said to be transparent; those kinds which, lying on the 
film, hindered the motion or threw it back were said to 
be opaque. 

The twisting motion round an axis was to them what 
electricity is to us. And when this twisting motion in 
one direction or another was conveyed to the particles 
of small masses which were free to move, many curious 
effects were produced analogous to the movements of 
electrified bodies. There are obviously no other rota- 
tions or vibrations possible ; hence in that world there is 
nothing corresponding to magnetism. Their light was 
simple, and could not be split into two kinds as our light 
can be into two kinds of polarized light. 

Was there no sign, then, by which the inhabitants of 
this world could gain a knowledge of their own limita- 

A Plane World. 155 

tion ? There was. There was both a sign and the inter- 
pretation of it lying before them. They knew that they 
could have two triangles precisely similar, and yet such 
as could not be turned the one into the other by any 
movement in the plane. How two things could be so 
alike, and yet differ in some mysterious way, was to them 
a puzzle. As an instance of such triangles may be 
taken those used in Diagram VI. to represent the man 
and the woman. They may be exactly equal, yet the 
beings in a plane world cannot turn them so that one 
would coincide with the other. 

Yet had they but considered the case of a being 
lower in the scale of space existence than themselves, 
they would have seen the answer to their riddle. 
For consider a being confined altogether to a line 

C' B' A' M A B C. Let M be the bein g> and 
let him observe the three points ABC, and let him 
form an idea of them and their positions with regard to 
each other, which he measures by the distance he has 
to travel to reach one after passing the other. 

Let him also become aware of the three points A' B' 
C', forming a precisely similar set on the other side of 

It may be objected that the being in the line could 
not conceive any point lying beyond A, but that his 
experience would be limited to the points A and A'. If 
A and A' are material particles this would be the case, 
but we may suppose them to be places in the line 
marked out by cold and heat, or some such means. 
Then a being could conceive a series of positions in his 
space such as A, B and C, A', B', C'. 

If now he remembers each set, and thinks about them, 
he finds that they are alike in every respect. But he 
cannot make them coincide with each other. For if he 

156 A Plane World. 

pushes the set A B C along the line, when A B and 
A' B' are together C is just where it ought not to be. It 
is not on C'. And if he gets C on C', then A B has gone 
far away. 

He would neither be able to make them coincide nor 
to conceive their coincidence. 

There would be no movement within the realm of his 
experience which would make them coincide. 

Yet the dweller in a plane world could easily make 
these sets of points coincide, for he would bend the 
whole line round in his plane so that A coming on A', 
B should come on B', and C on C'. There would be no 
difficulty to him in doing this. And he does it in virtue 
of there being to him a movement possible which is not 
possible to the being in the line. He has a liberty of 
motion unknown to the linear being. 

And now why should he not reason thus, " Something 
which to the linear being is inconceivable, to me is con- 
ceivable. Then may not things inconceivable to me be 
yet possible ? May it not be possible that two triangles 
which are like one another, but yet which cannot be 
thought by me as coinciding may not these triangles 
be able to be made coincident " ? 

In this simple fact of his perpetual observation was 
really the proof of the whole matter if he had but looked 
at it, the sign manual of his limitation, the promise of 
his liberation from it in thought, the key to the explana- 
tion of the mysterious minute actions by which he was 
surrounded, and perchance a help to the comprehension 
of a higher life. 


[|N our world a particle of matter which sends 
forth influence on the surrounding matter 
does not send its radiant energy off along a 
plane, but from the particle all the influence 
spreads out into space. And the most convenient in- 
stance in our world to consider is that of a luminous 
point from which rays spread out in every direction. 
Let M in Diagram XL be such a point a particle of 


A E 

Diagram XI. Particles in space and in a plane exerting force. 

matter sending forth luminous rays in our three-dimen- 
sional space. 

Instead of studying how these rays spread out in every 
way all around M, let us only consider those which, pass- 

158 A Plane World. 

ing out from M, fall on the square ABCD. ABCD 
casts a shadow, and this shadow extends, and is found to 
be bigger the further off from M it is measured. Suppose, 
at the distance from M, M E, we put a square in the path 
of the shadow so as just to receive the shadow on it 
exactly. Let E F G H be this square. As is shown 
by the dotted lines, this square will be four times as 
large as the square ABCD. So when the distance is 
doubled, the shadow becomes four times as big. 

Now those rays of light which fall on A B C D would, 
if they were not interrupted by it, spread out so as to 
exactly cover E F G H. Thus the same amount of 
light which falls on the small square ABCD would, if 
it were taken away, fall on the large square E F G H. 

Now since the large square is four times the size of 
the small square, and the same amount of rays fall on it 
for it only receives those which would fall on the small 
square there must be at any part of it an illumination 
one-quarter as strong as there would be at any point on 
the small square. 

Thus the small square, if placed in its position, would 
seem four times as bright as the large square. 

Thus, when the distance from the origin of light is 
doubled, the amount of light received by a surface of 
given area becomes one-fourth of what it was at the less 

This is what is meant by varying inversely as the 
square of the distance. When the distance is doubled 
the intensity of the light is not simply less, but is halved 
and halved, and becomes one-quarter of its previous 

But in the case of a particle resting on a thin sheet of 
metal, and shaking the metal as, for instance, a metal 
plate can be made to shake by a violin bow then this 
law would not hold. 

A Plane World. 159 

Take the second figure. Let P be the particle, and 
let the influence proceeding from it fall on the rod A B 
lying on the plane, and let us suppose the rod to stop 
the vibrations from going beyond it, to receive them and 
to turn them back just as a body does the light. Then 
the " shadow " of A B would spread out away from P ; 
and if another rod E F were put in at the distance P E, 
which is double of P A, then, to exactly fit the shadow, 
it would have to be double the length of A B ; and the 
vibrations which fell on A B would exactly fall on E F. 
Now since E F is twice as long as A B, the vibrations 
which fall on any part of it will be one-half as intense as 
the vibrations which fall on a portion of matter of the 
same size lying where A B lies. 

Thus in a plane the influence or force sent out by any 
particle would diminish as the distance. It would not 
' vary inversely as the square of the distance," but would 
:< vary inversely as the distance." 



JT seems to me that the subject of higher space 
is becoming felt as serious, and fraught with 
much that is of the deepest interest, not only 
as a scientific problem, but in other ways also. 

It seems also that when we commence to feel the 
seriousness of any subject we partly lose our faculty of 
dealing with it. The intellect seems to be overweighted 
somehow, and clogged. Perhaps the suppositions we 
make seem to us of too great importance, and we are 
not willing enough to let them go, fearing to lose the 
thing itself if we lose our hold of the means by which we 
have first apprehended it. 

But whatever may be the cause, it does seem un- 
doubtedly the fact that the mind works more clearly 
and more freely on subjects which are of slight im- 

And I propose, that without ignoring the real im- 
portance of the subject about which we are treating, 
we should cast aside any tension from our minds, and 
look at it in a light and easy manner. 

With this object in view let us contemplate a certain 
story which bears on our problem. 

It is said that once in a certain region of Ireland 
there took place a curious contest. For in Kilkenny 


1 62 A Picture of Our Universe. 

there were two cats so alike in size, vigour, determina- 
tion, and prowess, that, fighting, they so clawed, scratched, 
bit, and finally devoured each other, that nothing was 
left of either of them save the tail. 

Now, on reflecting on this story, it becomes obvious 
that it originated when looking-glasses were first im- 
ported into Ireland from Italy. For when an Irishman 
sees for the first time anything new, he always describes 
it in an unexpected and yet genial and interesting 
manner. Moreover, we all know what contentious fel- 
lows they are, and how all their thoughts run on fight- 
ing. And I think if we put this problem to ourselves, 
how by bringing in fighting to describe a looking-glass, 
we shall see that the story of the Kilkenny cats is the 
only possible solution. For consider evidently how it 
arose. Depositing his favourite shillaly in a corner, the 
massively-built Irishman, to whom the possession was a 
novelty, saw reflected in his looking-glass the image of 
his favourite cat. With a scrutinizing eye he compared 
the two. Point for point they were like. " Begorra if I 
know which of the two would win ! " he ejaculates. The 
combat becomes real to him, and the story of the Kil- 
kenny cats is made. 

Now, to our more sober mind, it is obvious that two 
cats two real material things could not mutually an- 
nihilate each other to such an extent. But it is perfectly 
possible to make a model of the Kilkenny cats to see 
them fight, and to mark the issue. 

And I propose to symbolize or represent the Kilkenny 
cat by a twist. Take a pencil, and round it twist a strip 
of paper a flat spill will do. Now, having fastened the 
ends on to the pencil by two pins, so that it will not un- 
twist, hold the paper thus twisted on the pencil at right 
angles to the surface of a looking-glass : and in the look- 
ing-glass you will see its image. In Diagram L, M repre- 

A Picture of Our Universe. 163 

sents the mirror, and on the left hand is shown the twist, 
on the right hand the image twist. Now take another 
pencil and another piece of paper, and make a model of 
what you see in the glass. You will be able to twist this 
second piece of paper in a spiral round this second pencil 
so that it is an exact copy of what you see in the glass. 
Now put the two pencils together end to end, as they 
would be if the first pencil were to approach the glass 
until it touched it, meeting its image : you have the real 
copy of the image instead of the image itself. Now pin 
together the two ends of the pieces of paper, which are 
near together, and you have your two Kilkenny cats 
ready for the fray. To make them fight (remember that 
the twists not the paper itself, but the paper twisted 
represent the cat), hold firmly and pull the other ends (the 
tail ends, so to speak), so as to let each twist exercise its 
nature on the other. 

You will see that the two twists mutually annihilate 
each other. Without your unwrapping the paper the 
twists both go, and nothing is left of them. 


Diagram I. 

Now the image of the twist as a real thing was made 
by us. It did not exist in nature other than as a mere 

But I want you to imagine this process of producing 
a real image as somehow existing. I want you to lay 

164 A Picture of Our Universe. 

aside for the present the question of how it could be 
done, and to conceive twists and image twists. 

This is the mechanical conception I wish you to adopt 
there are such things as twists. Suppose by some means 
to every twist there is produced its image twist. These 
two, the twist and its image, may exist separately ; but 
suppose that whenever a twist is produced its image 
twist is also produced, and that these two when put 
together annihilate each other. 

With this conception let us explore the domain of 
those actions which are called electrical. 

When a glass rod is rubbed with silk it becomes 
excited, its state is different. It manifests many pro- 
perties, such as that of attracting light bodies, giving off 
a glow of light, &c. The silk also with which it was 
rubbed manifests similar properties. It also attracts 
light bodies, appears to glow in the dark, &c. 

And yet there is a difference between the state of 
excitement of the glass and of the silk. The electricity 
which is in them is of different kinds. And if the 
electricity of the silk and of the glass be brought together, 
all electrical effect disappears ; they become glass and 
silk in an ordinary condition. 

It may seem strange that, if this is so, they should 
become electrified when rubbed together. Yet this is 
the case, and must be taken as a fact. It seems to 
depend partly on the circumstance that glass and silk 
are not what is called conductors. In a conductor, if 
one part receives electricity, this electricity at once runs 
over the whole of the conductor, whether it be an inch 
long or many feet. And if any part of the conductor 
be touched by another conductor which is in contact 
with the earth, every trace of electricity leaves the con- 
ductor, flowing, as it were, freely out of it. 

Now both glass and silk do not let the electricity run 

A Picture of Our Universe. 165 

from them so easily. To discharge a glass rod it nas 
practically to be touched in every part. Thus, when by 
the rubbing with silk electricity is produced on it, it is 
conceivable that this electricity should be kept to a 
certain extent, and not combined immediately with the 
electricity on the silk. 

Besides, the same cause the friction which produced 
the electricity on the glass, and the other kind of elec- 
tricity on the silk would probably prevent their com- 
bination as long as it was applied. 

Now let us suppose that the electrical charge which 
the glass has consists in this. 

Let us suppose that the particles of the glass on the 
surface of it are twisted, strained out of their natural 
position, and twisted. 

Let us also suppose that the particles of the silk are 
twisted too, but let them have the image twist. 

Now these two twists, the glass twist and the silk 
twist, its image, when brought together, will run down. 
In unwinding each other they will give off a certain 
amount of energy, which will manifest itself as a spark, 
make a crackling sound, and so on. But when they 
unwind each other there is no more tension of the 

This does not explain in the least why the glass 
particles should receive a twist in one direction, the silk 
particles a twist of the image kind. 

But instead of inquiring into this, it is best to see if 
this supposition is in accordance with other known facts 
of electrical action ; because, if it is not, we may dismiss 
it more easily than we could ^f we had to test it with 
regard to the very inaccessible question of why some 
bodies, when rubbed, get electrified in one way, others 
in another. 

When the glass and silk are near together tne twist 

1 66 A Picture of Our Universe. 

on the glass and that on the silk are related to each 
other as twist and image twist, and there is no action on 
surrounding bodies from either of them, as they, so to 
speak, satisfy each other. 

But when the glass rod and the silk are moved apart, 
and brought near other objects, then each of them calls 
up on those objects near which it is brought a twist of the 
kind which is the image of its own twist. 

If the glass rod is brought near a mass of metal, 
which we will call a conductor, the following effect is ob- 
served : The part of the conductor near the glass rod 
becomes charged with electricity of the silk kind ; the 
part of the conductor away from the rod becomes 
charged with electricity of the glass kind. 

Now let us bring into play the supposition which we 
made before. 

Let us suppose that there is some process in nature 
which, when there is a twist, makes a real image of that 
twist come into being. If we assume this process, we 
see that, opposite to the silk, on whatever objects are 
near it, will be a twist of the glass kind, and opposite 
the rod will be a twist of the silk kind. That is to 
say, that on the conductor there will be a twist of the 
silk kind when the glass rod is brought near it. 

But there is nothing to make the particles of the 
conductor twist as a whole. The glass rod is not sup- 
posed to touch the conductor it is simply brought near 
it, and no actual communication takes place between 
them. No force is actually applied to it, nor electricity 
communicated to it. Hence, on the whole, the particles 
of the conductor will not be twisted. That is to say, 
since there is a twist of the glass kind on one end, there 
will be at the other end a twist of the image kind that 
is, of the silk kind. And these two twists are like the 
two twists on the pencil if allowed to run together they 

A Picture of Our Universe. 167 

will run each other out. So if the conductor were re- 
moved from the neighbourhood of the glass rod it would 
be found to be no different from what it was at first, it 
would not be " charged." 

Now this is what actually happens. 

Thus we have, firstly, a glass rod with its twist ; 
secondly, a mass of metal with two twists on it one 
near the glass rod, and of the image kind ; the other at 
the other end of the mass of metal, and related to the 
original twist in the following way. It is the image of 
its image. 

Now it will be found by using a mirror that the image 
of the image of a twist is the twist itself. 

Hence on the other end of the conductor there is a 
twist of the same kind as that on the glass rod. 

And it is obvious that the rod, with its twist, is con- 
nected with the twist on the conductor nearest to it, and 
the twist on the other end of the conductor will, by the 
same arbitrary process which we have assumed as real, 
call up a twist, the image of itself, on any object near it. 

If it is touched by the object with this contrary twist 
the two will run together, and the conductor will, if it is 
left free, have only one twist the silk kind, which has 
come up opposite the rod. 

If now the rod be moved away, the conductor will be 
twisted as a whole ; that is, all the particles of which it 
is composed will be slightly twisted with a twist of the 
silk kind. 

In this state it is said to be charged. 

Thus the assumption which we have made, that there 
is some process in nature in virtue of which, opposite 
to any twist, its image twist is produced as a real thing 
this assumption is in harmony with tne laws of 

Instead of working with a glass rod it is more con- 

1 68 A Picture of Onr Universe. 

venient to use a metal rod. Suppose we take a poker 
and attach a handle of sealing wax to its middle. See 
A B below. This will be easily imagined, and its two 
ends, the handle and the black end, will be easily re- 
tained in the mind. 

If now electricity be communicated from the glass 
rod to the poker by touching the two together, what 
happens is this : The particles of the glass being twisted 
communicate their twist to the particles of the poker. 
The twist on the poker is of the same kind as the 
twist on the glass rod, and the amount of twisting 
which the glass particles had is divided between the 
glass rod and the poker. The use of the sealing-wax 
handle is to keep the twist from communicating itself 
to the body of the person holding it, and, through him, 
to the earth. It is found that certain bodies, " non- 
conductors," will not communicate the twist and convey 
it along ; whereas metallic bodies, and conductors 
generally, will communicate this twist at once to great 

We will suppose that a metallic body consists of par- 
ticles so arranged together that it easily acts as a set of 
minute threads or chains of particles which will twist, 
each thread or chain twisting as a whole. Thus the 
conception which should be formed of a metallic body 
conducting electricity along it is this : Conceive a 
bundle of very fine but very rigid wires, each wire twist- 
ing separately but with the same kind of twist as all the 
others, and each, as it twists, rotating amongst its fellow 
threads. If we have a metal rod we can twist it between 
the finger and thumb. This is not the kind of twist we 
suppose, but that each separate string of particles is thus 
twisted, so that each set twisting remains in the same 
part of the metal rod but is turning round in its fixed 
position. This is a body conveying an electric current. 

A Picture of Our Universe. 169 

If the current will not pass, the set of minute wires 
must be conceived as held at the far end, and given a 
twist, starting from the point where the electricity is 
communicated. Now if a conductor is thus charged and 
left, it is found that it retains its charge ; to be dis- 
charged it must be touched with another conductor. 
Hence this twist of minute threads differs from a twist 
of a wire in that the threads cannot untwist of them- 
selves unless other threads come into contact with them 
to which they can impart the twist. That this should 
be the case may depend on the fact that the twisting 
strings are strings of molecules, and the ends of them 
would thus be connected with other molecules with 
something of the same tenacity as that with which the 
strings themselves cohere together, and are unable to 
unlock themselves from these insulating or untwisting 

Let us consider the state clue to these twisting strings 
of particles. 

Place two pennies lying on the table before you, and 
suppose them to be the sections in which two strings of 
a conductor are cut across, so that you are looking at 
two particles, represented by the pennies in the interior 
of a conductor ; the strings, of which the pennies are 
sections, come up towards your eye. Now twist the two 
pennies each in the same direction say that of the 
hands of a watch. From the outer edges you can take 
the motion off; the edges are moving in the same direc- 
tion. But where the two pennies meet you will see that 
the edge of each is going in a contrary direction to the 
other. And if one penny tends to move an object in 
one way the other tends to move it in the contrary 
direction. Hence th^e mot-ions te n d to neutralize each 
other in the interior of a conducting wire. 

Having now formed a conception of the state of the 

170 A Pictiire of Our Universe. 

particles in an electrified poker, suppose another poker 
likewise held by an insulating handle is brought near 
the first. Let the pokers be so arranged that the 
handles both point one way, the black ends another way, 
and let the second poker be in the same line as the 
first, with its handle towards the black end of the first 

Now the first poker is charged, it contains electricity, 
its particles are twisted. What effect will it have on the 
second poker? 

It is found that the second poker undergoes a certain 
change, but when it is removed to a distance from the 
first poker all trace of this change disappears. 

On the end nearest the first poker on the handle is 
found silk electricity ; on the end furthest from the first 
poker on the black end is found glass electricity. 

A B C D 

+ + + 

Let A B be one poker, the + representing the charge of glass electricity. 
Let C D represent the other poker, the representing the induced 
silk electricity, the + the glass electricity in it. 

Let A be the handle of the first, B its black end. Let 
C be the handle of the second, and D its black end. To 
explain this let us bring in our imaginary principle. 
Let us suppose that when a charged body is brought 
near an uncharged body, but is separated from it by 
some medium through which electricity cannot pass let 
us suppose that by some agency the twist in the charged 
body calls up an image twist in the body opposite it 
Thus, due to the twist in the first poker there will be an 
image twist in the handle part of the second poker. 

But the strings of particles in the second poker are 
not twisted as a whole; they are twisted in such a 
way that if they are removed from the first poker, the 
twist, whatever it be, disappears. 

Now this would obviously be effected if we suppose 

A Picture of Our Universe. 171 

the same thing to go on in the second poker as took 
place between the first poker and the second. Let the 
twist in the handle end C of the second poker be accom- 
panied by the production of an image twist in the black 
end D. And let us take this as a fair account of our 
observations. If a body, which as a whole does not 
undergo a twist, has one part of it twisted, then 
there will be the image twist in the other part of it. 
1 say that the poker as a whole is not twisted, and all 
that this means is that if it be removed from the elec- 
trical influence it is found to be not charged ; and the 
idea which we may form is this : the strings of particles 
are twisted like the two strips of paper round the pencil ; 
they are twisted so that they will exactly unwind if left 

Now of course all these suppositions are merely pro- 
visional, and must be dismissed unless seen to be 
mechanically possible ; but for the present we are trying 
to see if our assumption will fit in with facts. And our 
assumption is that there is in nature a power which 
amongst the molecules produces that as a real thing 
which in our larger mode of existence only occurs as a 
simulacrum and appearance. Our looking-glass images 
are not real, but we suppose that real images are 
produced amongst the molecules. 1 

We have seen that if we make a certain supposition as 
to the calling up of an image twist by a twist of 
molecular matter, then the main facts of electricity are 
capable of an explanation, which, involving merely the 
motion of ordinary matter, is far preferable to the idea 
of there being a mysterious fluid, and more in harmony 
with our present ideas of electricity. 

And yet it is impossible to retain this supposition 
unless a clear mechanical explanation can be given of 

* For details, see Appendix III. 

\J2 A Picture of Our Universe. 

how a real image of itself can be called up by the twist 
which we suppose electricity to be. 

We can by intelligent agency produce a twist which 
is the real image of a given twist. But it would be 
absurd to suppose amongst the molecules an agency 
which, acting with prescribed aim, gave in that domain 
those real simulacra, those evident images, those phan- 
toms with which we in our larger world of masses are 
for ever mocked. 

And yet it would be curious if such an hypothesis 
were to claim a recognized position in our mental 
apparatus with which we think about nature. 

For in that molecular world, if we imagine it to our- 
selves, there would be a curious state. 

If we consider a twist and its image, they are but the 
simplest and most rudimentary type of an organism. 
What holds good of a twist and its image twist would 
hold good of a more complicated arrangement also. If 
a bit of structure apparently very unlike a twist, and with 
manifold parts and differences in it if such a structure 
were to meet its image structure, each of them would 
instantly unwind the other, and what was before a 
complex and compound whole, opposite to an image of 
itself, would at once be resolved into a string of formless 
particles. A flash, a blaze, and all would be over. 

To realize what this would mean we must conceive 
that in our world there were to be for each man some- 
where a counter-man, a presentment of himself, a real 
counterfeit, outwardly fashioned like himself, but with 
his right hand opposite his original's right hand. Exactly 
like the image of the man in a mirror. 

And then when the man and his counterfeit met, a 
sudden whirl, a blaze, a little steam, and the two human 
beings, having mutually unwound each other, leave 
nothing but a residuum of formless particles. 

A Picture of Our Universe. 173 


WHAT physical explanation is possible ot this produc- 
tion of a real image ? 

First of all we may note that the production of a real 
image of any disturbance is one of the commonest phe- 

If a piece of indiarubber lying on the table be pressed 
downwards with the finger it will move up when the 
finger is removed. The yielding and the resuming its 
original form are movement and image movement. 

If the disturbance is simply a displacement in one 
line, then, if the medium in which this displacement is 
produced is not permanently displaced, but on the whole 
maintains its equilibrium, there invariably accompanies 
any displacement its image displacement. 

Moreover, to take the simple example of a wave propa- 
gated through water the particles of the water on the 
whole move about a mean position ; they are not displaced 
permanently in any one direction ; and, taking the dis- 
tance from the crest to the hollow of a wave, then from 
the hollow to the next crest, is the real image of the first 
part. Thus in the complete movement in the wave 
measured from crest to crest, there is displacement and 
its real image. 

Thus there seems some consistency about this suppo- 
sition of an image, about the production of a real image 
in nature. 

But there are two observations which we can make. 

Firstly, if it is true in these complicated cases it ought 
to be true in simpler cases also. That is, it this suppo- 
sition is in harmony with electrical actions, it ought to 
tit in with other actions of a simpler kind. 

Secondly, a supposition of this kind has no per- 

1 74 -A Picture of Our Universe. 

manent value ; it is rather a feeler, by which we trace 
out our way in the darkness, than any actual vision 
itself. In default of an actual realization of what the 
electrical relations are we can treat them by means of 
a supposition. But we must be ready at any moment 
to give up the supposition if it does not harmonize with 
the facts. 

And in the first case does the idea of a real image 
hold good about the simplest possible actions ? 

If we push our fist towards a glass the image is that of 
a fist moving in the opposite direction. 

Now, suppose a pressure exerted on a wall, as, for 
instance, a hard stone hitting it. The wall undergoes a 
displacement, but not as a whole only that part of it 
where the stone hits. And this displacement is followed 
by the image displacement, for the wall in the part 
where it has been hit and pressed back moves forward, 
and by its reaction throws the stone off. 

Every case of action and reaction is a case of a motion 
and its image motion. 

If a bullet strikes the wall and goes with such velocity 
that it lodges in it, then the motion of the ball and the 
image motion of the wall destroy one another, and the 
result is a shattering of the wall in the path of the bullet. 

Now in the case of a simple displacement of this kind 
there is a rule by which we can form the image dis- 
placement. Take a point on the wall, and about this 
point as a centre turn the displacement half way round, 
so that it does not come to be itself again, but is oppo- 
site to itself. 

By this turning, the displacement becomes the image 
ot itself; a movement into the wall becomes a move- 
ment out from the wall ; and these follow one another if 
the wall is not injured. It should be noticed that the 
displacement is moved round this point, using a direction 

A Picture of Our Universe. 


which is not in the displacement itself. The displace- 
ment goes straight into the wall. The turning motion, 
which we suppose, needs another direction than this. 

Now suppose, instead of a simple displacement like 
this, we take a displacement involving two directions, as 
in the case of a wave disturbance it will be found that 
the conditions are just the same. If a wave movement 
falls on a medium which it does not destroy or move as 
a whole, the displacement calls up its image displace- 
ment. And the image displacement can be found, as 
before, by twisting the displacement round so as to be- 
come opposite to itself by twisting it half-way round. 
But in this case, too, a direction must be used which is 
not used in the displacement itself. 


Diagram II. 

Let us look at the wave disturbance more closely. 

The horizontal central line in Diagram II. will re- 
present the positions which a number of particles occupy 
when at rest. That is, let us suppose there to be a num- 
ber of particles lying in a series forming this line. 

We can think of the portions of an elastic cord. An 
indiarubber tube may be taken as an illustration, and 
made to vibrate by a motion of the hand. 

If now one of the particles be deflected from its 
natural position suppose it is moved to the position 
M then we should have one particle at M out of its 
place, and all the others in their places. 

But this does not happen. If the particle is pulled to 


176 A Picture of Our Universe. 

M, the particles near it follow after it, and are also dis- 
turbed from their places, though not so much as the 
particle at M. 

We should have a set of particles forming a shape 
like L M N, only much longer ; in fact, the particles all 
along the cord would be raised. 

If the cord is struck suddenly we do have a set 
arranging themselves like L M N, but only for a limited 
distance along the cord. 

And here we notice a curious thing. 

If a set of particles is forced to go like L M N, 
removed from their position of repose, then at once a 
set of particles goes like N O N'. 

A displacement is accompanied by another displace- 
ment which is the opposite of it. And this displacement 
and opposite displacement travels along the elastic cord. 

But the point of view which is the most natural one 
to regard it from is a little different from this. Let us 
consider a single point, P. When this is disturbed it 
moves above its original position to M, and below to 
the other end of the dotted line. Its complete move- 
ment is from one of these extremes to the other. And 
if we take the complete disturbance as exhibited in all 
its phases by different points, we ought to look at the 
portion of the diagram M N O. For here at N we have 
a point not displaced at all ; at M, one displaced to its 
full extent upwards ; at O, one displaced to its full extent 
downwards. And intermediate particles have interme- 
diate displacements. 

Now when a complex displacement of this kind is put 
into a cord, its image at once springs up. The displace- 
ment represented by M N O at once calls up the dis- 
placement represented by O N' M', and this condition of 
displacement and image displacement continues repeat- 
ing itself till the cord comes to rest. 

A Picture of Our Universe. 177 

If the diagram be closely looked at, it will be seen 
that it exhibits the image relationship twice over. For 
the movement of the particle P from P to M has its 
image in the motion of another particle from its place 
of repose to the position O. The disturbance itself, 
M N O, consists of displacements and image displace- 
ments ; and this disturbance, with its image O N' M', 
makes the wave from crest to crest. 

The "twist" which we consider in these pages is like 
the wave motion, but with a third component added, so 
that in the complete motion there is a displacement 
coming out from the plane of the paper, as well as the 
displacements in the plane of the paper itself. 

And just as the wave displacement produces a real 
image of itself in a medium which it does not distort as 
a whole, so there is nothing arbitrary in our assuming 
that an electric twist calls up the real image of itself 
in an insulating medium that is, a medium which it 
cannot twist as a whole. 

If L M N O is a wave motion, then L' M' N' O is its 
image, as produced by moving it round out of the plane 
of the paper Diagram II. If the wave disturbance is 
moved round in the plane of the paper, the original wave 
L M N O becomes L' M' N' O Diagram III. a shape 
which bears no resemblance to the transmitted wave. 

Consider O N M L to be a bent piece of wire lying on 
the paper ; if it is moved round O, keeping on the paper, 
it becomes O N' M' L'. To become like O N' M' L' 
in Diagram II. it must move : tip from the paper and 
down again on the right. 

Thus adopting this artificial aid to thought that a 
displacement calls up an image displacement we get 
the rule that this displacement, the image, can be got 
from the original displacement by moving the original 
displacement half-way round, using as the plane in which 

I 7 8 

A Picture of O^lr Universe. 

the turning is made that plane which is given us by 
taking these two directions the direction in which the 
wave is moving, and a direction at right angles to the 
directions in which the displacements which form the 
wave take place. 

Thus, with the wave motion shown, if we take the 
direction towards the top of the page to be the up di- 
rection, and that from left to right to be the sideways 
direction, then out of the paper towards us is the " near " 
direction. So, too, in this case we have to turn the wave 
disturbance out of the plane of the paper, and each point 
of it, to produce the image, must turn in a circle (going 



Diagram III. 

half-way round it) lying in a plane which has the two 
directions near and sideways. The motions of the par- 
ticles themselves are in the plane of the paper. So to 
get the image by turning we use a direction the 
"near" direction, which is not involved in the wave 
motion itself. 

Hence we may state, as a tentative principle, that 
when a disturbance takes place in a medium which will 
not be disturbed as a whole, then such disturbance is ac- 
companied by a real image of itself; and this real image 
of itself is the configuration which would be obtained by 
twisting the original disturbance round in a direction not 
contained in the original disturbance. 

A Picture of Our Universe. 179 

Thus the disturbance O N' M' L' is obtained by twist- 
ing the disturbance L M N O round. The direction in 
which it is twisted is the direction coming out from the 
plane of the paper. 

Now if this plane disturbance is in nature accompanied 
by its real image, why should not a twist such as takes 
place in the electric current also be accompanied by its 
image twist when it impinges on a medium which it 
cannot twist as a whole that is, when it comes to an 
insulator in its path ? 

The reason, obviously, is that we cannot conceive such 
an image produced mechanically. And the reason of 
this can be exhibited thus. 

When we had a plane disturbance like L M N O we 
only used up two dimensions of space, and we have a 
third coming up from the plane ; and this direction en- 
ables us to imagine a turning which will alter A B into 
its image. 

But when we have a twist proceeding along an axis, 
as in the case of electricity, we have no direction left 
over in space whereby we may conceive the twist turned 

Now when the displacement itself involves all these 
directions how will our rule hold ? 

How shall we get the image displacement ? We can 
find what it is by using a looking-glass ; but the same 
rule which served in previous cases ought to work here 

We want a direction which is neitner up and down, 
right and left, towards and away. 

Now let us adopt a mathematical device, and suppose 
there is such a direction, and let us call it the X direction, 
the unknown direction. 

Then if we turn the twist round, using this X direction, 
we shall get the image if our rule is correct. And as a 

180 A Picture of Our Universe. 

matter of fact, by twisting a figure round in this way, 
using a direction different from any of the three men- 
tioned above, we do get its image. 

Hence the rule we have formed works consistently. 

It will be found that if there was another direction so 
that the spiral disturbance could be turned independently 
of the directions used up in it, that just as a plane dis- 
turbance can be turned into its image disturbance, 
so the spiral disturbance of electricity could be turned 
into its image spiral by a simple turning. 

In this argument we have not looked at the matter 
directly, but from the outside. To see it immediately 
requires us to gain a familiarity with the properties of 
space with four independent directions, and that would 
take too long for the present paper. The same conclu- 
sion can be arrived at mathematically ; but in these 
papers as far as possible we avoid symbolism. We 
want to gain hold of scientific facts in a warm and 
living way, to unwrap them from conventionalities and 

Thus if we suppose that in the minute motions which 
go on about us there is a possibility-of moving in a four- 
dimensional way, then it is perfectly legitimate to assume 
that in a medium which cannot be twisted, but which is 
elastic, a twist calls up a real image twist. 

And thus the assumptions which we have made as the 
basis of an electrical theory are justified on the assump- 
tion of a four-dimensional space, are untenable except 
on that supposition. 

The matter is of course perfectly open. The only way 
is this, by adopting the assumption of a higher space to 
predict what the actions of the molecules will be, then if a 
number of predictions are verified the evidence will be- 
come strong. And I feel sure that there are some very 
curious things to be made out here. For my own part 

A Picture of Our Universe. 181 

the evidence of the reality of four-dimensional space in 
the sense in which we say that our space is real does 
not rest on the consideration of the molecular move- 
ments about which it is not easy to get clear ideas, 
but on the study of the facts of space. I hardly think 
that any one who spent a few years in becoming familiar 
with the facts of space, not by the means of symbolism 
or reasoning but by pure observation, could doubt that 
there are really four dimensions. 

In noticing the simpler actions and their image actions 
we find that the real image does not coexist with its 
original, but rather follows and succeeds it. If we push 
against a board the board yields, and springs back when 
we leave off pushing. If the original displacement is 
permanent as a point pressed against an elastic surface 
and making the surface yield, then the image of this 
displacement is potential ; it is not actually there, but 
comes into play as soon as the original displacement is 

Now in the electrical actions we have assumed both 
the original twist and the image twist as concurrently 

In certain cases there is no doubt that they are co- 
existent as when a glass rod is rubbed by silk. 

But if the case of the action of a charged poker on an 
uncharged one be examined it will be found that there 
is nothing to prove that the image twist comes into 
existence until the original one is removed. 

When the charged poker is brought near the other, 
the remote end of the second is affected with the same 
kind of electricity as is on the charged poker. 

The appearance is just the same as if a thin wall were 
exposed to a pressure on one side, and the other side 
were to bulge out. The displacement is transmitted 
through the conductor. 

1 82 A Picture of Our Universe. 

It is only when the original charged body is removed 
that the image charge is found to be in existence on the 
second conductor. There are some peculiarities, how- 
ever, which make electrical displacements different in 
their appearances from ordinary displacements. 

No body can be made to move in any direction with- 
out imparting an equal motion in an opposite direction 
to another body e.g., the motion of a cannon ball is 
equalled by the recoil of the cannon. 

And so no twist can be given to the particles of a 
body without an image twist being given to other 

Now the image displacement or rectilinear motion, 
in the case of a rectilinear motion, in straightforward 
movement seems to remain in the place where it was 
produced. The recoil of the gun carriage produces a 
strain on its bearings and friction, which produce heat, 
which gradually dissipates. 

But the image displacement, in the case of electricity, 
seems to have a marvellous facility for running through 
the earth and meeting the original displacement. An 
indefinitely long line of action seems in electricity to 
take the place of a simple point. Our ordinary mechani- 
cal forces are located in centres, or points of action. In 
electricity the line seems to take the place of the point. 
Where the ordinary engineer deals with points the 
electrical engineer deals with lines. 

A Picture of Our Universe. 183 



THERE are some expressions which, being somewhat 
vaguely used, are apt to cause confusion in the mind of 
those who read or hear about higher space. 

And perhaps the most mischievous is the expression, 
a curvature of space. Now of space as it is generally 
used, in its accepted significance, there can be no curva- 
ture. For space means a system of positions extending 
uniformly in the number of dimensions we choose to fix 

If we take the straight line as our space, we may call 
it i space ; then the set of positions follow one on after 
the other without bending. If the line is bent it becomes 
a line, not a straight line. It should not be called I 
space, but a thing in 2 space. That is, it is a bent line 
in a plane. 

A being who was on the line might not perceive the 
fact of this bending, and it might not affect the measure- 
ments he made. But if the line ran into itself again, and 
he found that he was moving on what we should call a 
circle, this would in no way affect his idea of space. 
He would recognize that what he called space, namely, 
his line, was not space, but a curved thing in 2 

Similarly, taking a plane this is by definition not 
curved in any way, known or unknown, and it can only 
be conceived to be bent by ampler space being conceived, 
and its being imagined as having force applied to it so 
as to become a bent thing in this ampler space. In this 
case the term " plane " is not the correct name. 

And so about our three-dimensional space ; we cannot 
be robbed of that idea, although it might conceivably be 

184 A Picture of Our Universe. 

proved that our earth and our whole universe were on a 
curved thing in 4 space. 

We will then keep the term " space " for the ordinary 
conception ; and call it I, 2, 3, 4 space, according to the 
number of supposed independent directions. 

A curved line or surface or solid we will call a I, 2, or 
3 thing, according to the number of dimensions in it. 

A straight line is a I thing possible in i space. A 
circle is a I thing possible in 2 space. At any point of 
it a being in it is limited to motion in one direction, 
while the circle itself involves two dimensions. The 
surface of a sphere is a 2 thing possible in 3 space. The 
rind of an orange, or the orange itself, is a 3 thing possible 
in 3 space. 

It will be observed that the surface of the sphere, 
although only a 2 thing, involves the conception of 
3 space, and cannot be understood without the use of the 
idea of 3 space. It is a 2 thing because at any point of 
the surface a being can only move in two independent 
directions. A crooked line drawn on the surface of a 
sphere is a I thing in a 2 thing in 3 space. 

Another very common misconception is occasioned 
by the use of a figure of this kind Q(^ to represent a 
" knot " in 2 space. 

It obviously corresponds in 2 space to an iron rod 
welded together at the crossing place of the loop, so that 
it is indistinguishable which is the one free end, which 
the other. At the crossing point the two lines repre- 
sented by the two ink marks must be absolutely one and 
the same. 

If one line be supposed to go over the other, by how- 
ever small a distance, it would leave the plane. It would 
suddenly become invisible to the creature in the plane, 
and it would appear again at the other side of the line it 
crossed as if it came from nowhere. 

A Picture of Our Universe. 185 

It would be as extraordinary a sight as if we saw a 
pole going up to a brick wall, then beyond the brick 
wall the rest of the pole appearing not going through 
the brick wall, nor coming round it but somehow 
appearing; part of the same pole moving when it 
moved, obviously connected with it, and yet with no 
joining part which we could possibly discover. 

Again, it sometimes appears to be thought that the 
fourth dimension is in some way different from the three 
which we know. But there is nothing mysterious at all 
about it. It is just an ordinary dimension tilted up in 
some way, which with our bodily organs we cannot point 
to. But if it is bent down it will be just like any ordinary 
dimension : a line which went up into the fourth dimen- 
sion one inch will, when bent down, lie an inch in any 
known direction we like to point out. Only if this line 
in the fourth dimension be supposed to be connected 
rigidly with any rigid body, one of the directions in that 
rigid body must point away in the fourth dimension 
when the line that was in the fourth comes into a 3 
space direction. 

If the reader will refer back to the paper on the plane 
world he will find a description of the means by which 
a being there might know that he was in a limited 
world, and that his conception of space was not of what 
was really the whole of space, but of the limited portion 
of it to which he was confined by his manner of being. 

The test by which such a being could discover his limi- 
tation was this. He found two things, each consisting of a 
multitude of parts two triangles ; and the relationship of 
the parts of the one was the same as the relationship of 
the parts of the other. For every point in the one there 
was a corresponding point in the other. For every pair 
of points in the one there was a corresponding pair of 
points in the other. In fact, considered as systems made 

1 86 A Picture of Our Universe. 

up of mutually related parts, each was the same as the 

Yet he could not make these two triangles coincide. 
Now this impossibility of bringing together two things 
which he felt were really alike was the sign to him of his 
limitation ; and by reflecting on the similar appearance 
which would present itself to a being limited to a straight 
line by thinking of two systems of points which were 
really identical, and which he could make coincide, but 
which a line being could not make coincide, he would 
be led to conclude that he in his turn was subject to a 

Now is there any object which we know which, con- 
sidered as a whole consisting of parts, is exactly like 
another whole, the two having all their parts similarly 
arranged, so as to form in themselves two identical 
systems, and yet the one incapable of being made to 
coincide with the other, even in thought ? 
Let us look at our two hands. 

They are (except for accidental variations) exactly 
alike. And yet they cannot be made to coincide. 

And here, if we reflect on it, is the sign to us that we 
are limited in our notions of space that we are really 
in a four-dimensional world. 

Watching a ship as it recedes from the shore we see 
that it becomes hull down before it vanishes, and know 
that the earth is round. And no less certainly do our 
two hands, in their curious likeness and yet difference, 
afford to us a perpetual proof of our limitation, and 
indicate a larger world. 

This sign really tells us more than the mere fact 
of our limitation : it tells us where to look for the 
possibility of four-dimensional movements. It tells us 
that movements of any degree of magnitude relative to 
us are not possible in the fourth dimension. It tells us 

A Picture of Our Universe. 187 

to look for four-dimensional movements in the minute 
particles of matter, not in the movements of masses of 
about our own size. 

The task before us is difficult. We have to make up 
from the outside what the appearances of a higher space 
existence are to us in our space, and then we have to 
look at the facts of nature and see if they correspond to 
these appearances. 

Let us take a few isolated points and look at them 

To a being standing on the rim of a plane world a 
straight line absolutely shuts out the prospect before 
him. If the straight line is infinite it cuts his world in 
two ; he can never hope to get beyond it. 

It is to him what an infinite plane would be to us, 
stretching impassably in front of us, cutting us off from 
all that lies on the other side. 

But we know that a point can move round this line. 
It can revolve round it by going out of the plane, and 
coming down again into the plane on the other side of 
the line. 

This movement would be inconceivable to a plane 
being ; for he can only conceive it possible to get to the 
other side of the line by going to the end of it and 
coming back along the other side of the line. 

Now take a piece of paper and put a dot right in the 
middle and suppose that it has no means of passing 
through the paper. We can only conceive the dot get- 
ting to the other side of the paper by passing round the 
edge and coming back again to the position underneath 
where it was. 

But by a four-dimensional movement it can slip round 
the paper without going to the edge. 

A set of words may help. In a plane a body rotates 
round a point rotation takes place round a point. In 

1 88 A Picture of Our Universe. 

space rotation is always round a line the axis. In 
four-dimensional space rotation takes place round a 

To take a farther consideration of this point a plane 
being can see one side or the opposite of a straight line. 
He can only see it in one direction or in the reverse 
direction. But we can look at a straight line from a 
direction at right angles to that in which a plane being 
looks at it. We can look at a straight line from points 
which go all round it. 

Similarly, a being in four-dimensional space can look 
at a plane from a direction at right angles to that in 
which we look at it. If we try to think of this we shall 
imagine ourselves looking at the thin edge. But this is 
not what a four-dimensional being would mean. He 
would see the plane exactly as we see it, but it would be 
from a direction at right angles to that in which we look. 

In working with four-dimensional models it is a curious 
sensation until we become used to it that of looking at 
a plane at one time, and then looking at it again ; and, 
although it seems just the same as square in front of 
us as before realizing that we are looking at it from a 
direction at right angles to that of our former view. 

And in four dimensions a point which is quite close 
to a plane can revolve round it without passing through 
it, thus presenting to us the appearance of vibrating 
across the plane, but not passing through it. 

The appearance is as wonderful to us as it would be 
for a plane being to see a point which was in front of 
a line quickly passing behind it without having gone 
round the end. Such a point would appear to the plane 
being to vibrate across his line without passing through it. 

Now if we stand in front of a mirror we see the image 
of ourselves. If we were to go round the mirror and 
take behind it the position which our image seemed to 

A Picture of Our Universe. 


occupy, we should not be able to make ourselves co- 
incide with it. In the mirror opposite to our left hand 
is the image of our left hand ; but if we passed round, 

Diagram IV. 

our right hand would be in the place in which we 
imagined we saw the image of our left hand. And thus 
we cannot make ourselves coincide with our image. But 
by a rotation in four-dimensional space we could put 

Diagram V. 

ourselves so as exactly to coincide with our image. 
This can be seen by referring to the case of the straight 
line, Diagram IV. 

190 A Picture of Our Universe. 

Let A B C be a triangle, and G a line. If A U C 
moves round the end of the line, it can take up the posi- 
tion A' B' C' ; but it cannot anyhow be made to take the 
position shown in Diagram V., A' B' C'. 

But if we move the triangle ABC out of the plane 
round the line G as axis, it will, in the course of its 
twisting round this axis, come into the position A' B' C' 
It will come into this position when it has twisted half- 
way round. The point A, for instance, twists round in 
a circle lying in a plane which contains the direction 
A to A', and the direction at right angles to the paper. 
Twisting half-way round in this circle, it becomes A', 
and so on for the other points. Now a being who did 
not know what a direction was which lay out of the 
plane would not be able to conceive this twisting and 
turning movement. It would be as impossible for him 
to conceive the triangle ABC turned into the triangle 
A' B' C', as it would be for us to suppose ourselves 
turned into the looking-glass image of ourselves by a 
simple twisting. 

Yet just as a thing inconceivable to the plane creature 
can be done, so we could be twisted round and turned 
into our image. But this only holds theoretically ; our 
relation to the aether is such that we cannot be so turned, 
or any bodies of a magnitude appreciable to our senses. 

If we consider the case of a being limited to a plane, 
we see that he would have two directions marked out 
for him at every point of the rim of matter on which he 
must be conceived as standing. This is up and down, 
and forwards and backwards the up being away from 
the attracting mass on which he is. 

Now, if he were to realize that he was in three-dimen- 
sional space, but confined to a plane surface in it, his 
first conclusion would be that there was a new direction 
starting from every point of matter, and that this new 

A Picture of Our Universe. 191 

direction was not one of those which he knew. This 
new direction he could not represent in terms of the 
directions with which he was familiar, and he would have 
to invent new terms for it. 

And so we, when we conceive that from every particle 
of matter there is a new direction not connected with 
any of those which we know, but independent of all the 
paths we can draw in space, and at right angles to them 
all we also must invent a new name for this new 
direction. And let us suppose a force acting in a definite 
way in this new direction. Let there be a force like 
gravitation. If there is such a direction, there will pro- 
bably be a force acting in it ; for in every known direction 
we find forces of some kind or another acting. Let us 
call away from this force by the Greek word ana, and 
towards the centre of this force kata. Then from every 
point in addition to the directions up and down, right 
and left, away from and towards us, is the new direction 
ana and kata. 

Now we must suppose something to prevent matter 
passing off in the direction kata. We must suppose 
something touching it at every point, and, like it, 
indefinitely extended in three dimensions. 

But we need not suppose it this unknown to be 
infinitely extended in the new direction ana and kata. If 
matter is to move freely, it must be on the surface of 
this substratum. And when the word surface is used it 
does not mean surface in the sense that a table top is a 
surface ; it is not a plane surface, but a solid space sur- 
face. If from every point of a material body a new 
direction goes off, the matter which fills up the space 
produced by the solid moving in this new direction will 
have the solid it started from as its surface, and will be 
to it as a solid cube is to the square which bounds it on 
the top. 


192 A Picture of &itr Universe. 

Now this body which extends thus, bearing all solid 
portions of matter in contact with its surface by every 
point of them, may be thick in the kata direction or 

If it is thick, then the influence of any point streaming 
out in radiant lines will pass as in all space directions, 
so out also in this new direction. 

And then if its influence spreads out in this new 
direction, its effect on any particle near it will diminish 
as the cube of the distance ; for, besides filling all space, 
it will have also to fill space extended in this new direc- 

But we know that the influence proceeding from a 
particle does not diminish as the cube of the distance, 
but as the square of the distance. 

Hence the body which, touching all solid bodies by 
every point in them, and supports them extending itself 
in the kata direction this body is not thick in this 
direction, but thin. It is so thin that over distances 
which we can measure the influence proceeding from a 
body is not lost by spreading in this new kind of depth. 

Thus the supporting body resembles, as far as we 
know it, a portion of a vast bubble. But moving on the 
surface of this bubble we can pass up and down, near 
and far, right and left, without leaving the surface of the 
bubble. The direction in which it is thin is in a direction 
which we do not know, in which we cannot move. But 
although we cannot make any movements which we can 
observe with our eyes in this direction, still the thin film 
thin though infinitely extended in any way which we 
can measure this thin film vibrates and quivers in this 
new direction, and the effects of its trembling and quiver- 
ing are visible in the results of molecular motion. It 
only affects matter by its movement in directions at right 
angles to any paths which we can point to or observe, 

A Picture of Our Universe. 193 

and these movements are minute ; but still they are 
incessant, all -pervading, and the cause of movements of 
matter. It is smooth so smooth that it hinders not at 
all the gliding of our earth in its onward path. Hence 
it does not transmit a direct pull or push in any direction 
from one particle to another ; but by the tvvistings and 
vibrations of the material particles it is affected, and 
conveys from one to another these movements. Yet to 
bear up all matter, and thus hold it on its vast solid 
surface, it must be extremely rigid and unshatterable ; 
and hence it cannot be permanently altered or twisted 
by any force proceeding from matter ; but receiving from 
matter any push or twist, it is impressed with it for some 
distance ; then, reasserting itself, it produces an image 
displacement or twist, and this image it transfers to the 
particles of matter which it touches. 

Sometimes, as when light comes from the sun, this 
displacement and image is repeated and repeated in- 
numerable times before at last we, receiving it, become 
aware of the origin of the disturbance. 

But the properties and powers of this solid sheet 
this film quivering and trembling, yet infinite and solid 
are too many to begin to enumerate. The aether is 
more solid than the vastest mountain chains, yet thinner 
than a leaf ; undestroyed by the fiercest heat of any 
furnace, for the heat of the furnace is but its shaking 
and quivering ; bearing all the heavenly bodies on it, 
and conveying their influence to all regions of what we 
call space. 

And by some mysterious action it calls up magnetism 
from electricity ; by its different movements it gives the 
different kinds of light their being. 

Of itself untrammelled and unclogged by matter, it 
vibrates and shakes with the speed and rapidity of the 
vibrations of light. But when matter lies on it when air, 

194 A Picture of Our Universe. 

even in its rarest condition, lies on it its proper move- 
ment is damped and some of its quick shakings that are 
light, slow down to the obscure vibrations of heat. Thus of 
itself it will not take up the vibration of a hot body, but 
selects only those orbs which are glowing with radiant 
light wherefrom to take its thrilling messages. But 
when matter lies on it, it takes obediently the less 
vivacious movements of terrestrial fires. 

A being able to lay hold of the aether by any means 
would, unless he were instantly lost from amongst us by 
his staying still while the earth dashes on he would be 
able to pass in any space direction in our world. He 
would not need to climb by stairs, nor to pass along- 
resting on the ground. 

And such a being, even as thin as ourselves, and as 
limited, if not even in physical powers, but merely in 
thought he became aware of his true relation to the 
aether, he would see all things differently. 

From all shapes would fall that limitation of thought 
which makes us see them differently to what they are ; 
and in largeness and liberty of possible movement his 
mind would travel where ours but creeps, and soar and 
extend where ours journeys and diverges. 

It is impossible in contemplating the rudiments of 
four-dimensional existence to prevent a sense of largeness 
and liberty penetrating even through the profoundness 
of our ignorance. 

Whether we shall find beings other than ourselves, 
when we have explored this larger space, cannot be said. 

But there is a path which holds out a more distinct 

When the conditions of life on a plane are realized it 
becomes evident that much of that which is to us merely 
natural obvious from the very conditions of our life 
could only be attained by beings on the plane as the 

A Picture of O^tr Universe. 195 

result of artificial contrivances and modifications of their 
natural tendencies. In their progress and development 
they would, as it were, represent on the plane the features 
of the normal and undeveloped life of three-dimensional 
beings, and they would attain, as a result of moral labour 
and energy, a position which children in our higher life 
are born to without trouble or thought. 

And so we in our advancing civilization may to the 
eyes of some higher beings represent in our arrange- 
ments and institutions an approach to the simplest 
matters of fact in their existence. We are separated 
from such a view by our bodily conditions, but we 
are not to be prevented from taking it with our minds. 

By building up the conception of higher space, by 
framing the mechanics of such a higher world, we may 
arrive at a fairly accurate knowledge of the conditions 
of life in it. 

And then, with that element in our thought, with the 
reasoned-out characteristics present to our minds of 
what life on a higher physical basis would be, we may 
be able to judge amidst conflicting tendencies with more 
certainty and calmness. 

In one of the following papers of this series an account 
will be given of some of the facts which we can discern 
about the machinery and appliances of four-dimensional 

But the work of real discernment belongs to those 
who will from childhood be brought up to the concep- 
tion of higher space. 


SUPPOSITION can be made with regard to 
the aether which renders clearer an idea often 
found in literature. 

This idea is that of the freedom of the will. 
If the will is free, then it must affect the world so as to 
determine chains of actions about which the mechanical 
laws hold true. We know that these mechanical laws are 
invariably true. Hence, if the will is an independent 
cause, it must act so that its deeds produce to us the 
appearance of a set of events determined by our known 
laws of cause and effect. The idea of the freedom of 
the will is intimately connected with the assertion that 
apparent importance, command of power, greatness and 
estimation, are outside considerations, not affecting the 
real importance and value of any human agent. These 
ideas can easily be represented using the idea of the 
aether as here given. 

For suppose the aether, instead of being perfectly 
smooth, to be corrugated, and to have all manner of 
definite marks and furrows. Then the earth, coming in 
its course round the sun on this corrugated surface, 
would behave exactly like the phonograph behaves. 

In the case of the phonograph the indented metal 
sheet is moved past the metal point attached to the mem- 
brane. In the case of the earth it is the indented aether 
which remains still while the material earth slips along 

A Picture of Our Universe. 197 

it. Corresponding to each of the marks in the aether 
there would be a movement of matter, and the con- 
sistency and laws of the movements of matter would 
depend on the predetermined disposition of the furrows 
and indentations of the solid surface along which it slips. 

The sun, too, moving along the aether, would receive 
its extreme energy of vibration from the particular 
region along which it moved, and the furrows of the 
intervening distance give the phenomena actually observed 
of our relationship to the sun and other heavenly bodies. 

Thus matter may be entirely passive, and the history 
of nations, stories of kings, down to the smallest details 
in the life of individuals, be phonographed out accord- 
ing to predetermined marks in the aether. In that case 
a man would, as to his material body, correspond to cer- 
tain portions of matter ; as to his actions and thoughts 
he would be a complicated set of furrows in the aether. 

Now what the man is in himself may be left un- 
determined ; but he would be more intimately connected 
with the aether than with the matter of his body. And 
we may suppose that the aether itself is capable of 
movement and alteration ; that it moulds itself into 
new furrows and marks. 

Thus the old woman smoking a pipe by the wayside 
years ago, and whom I somehow so often remember, is 
not much different from me we are both corrugations of 
the same aether. 

Now our consciousness is limited to our bodily sur- 
roundings. Yet it may be supposed that in an action of 
our wills we, whatever we are (and for the present let us 
suppose that we are a part of the aether), we may be 
altering these corrugations of the aether. A single act 
of our wills, when we really do act, may be a universal 
affair with quite infinite relations. Thus it may be the 
immediate presentation to us of an alteration proceeding 

198 A Picture of Our Universe. 

from us of all that set of corrugations which represents 
our future life ; it may be the whole disposition and lie 
of events, which are prepared for the earth to phono- 
graph out, being differently disposed. And it evidently 
is quite independent of the particular furrows in which 
such alteration first occurs. That long strip of aether 
which is a very humble individual may, by an act of self- 
configuration, affect the neighbouring long strips and 
produce great changes. At any rate the intrinsic value 
of the will is quite independent of the kind of furrows 
along which any material human body is proceeding. 


IT is a good plan in fixing our attention to give de- 
finite names to the directions of space. Let U stand 
for up. Then the up direction we will call the U direc- 
tion, or simply U. 

Then sideways, from left to right, we will call V, so 
that moving in the V direction, or moving V, means 
moving to the right hand. 

Then the away direction we will call W, so that a 
motion which goes away from us we caJl a W motion, 
and its direction we call W. 

Then any other direction which we suppose indepen- 
dent of these we will call the X direction. Now the 
simple push or displacement takes place in direction V, 
or left to right. It is turned into its image by turning 
in the plane U V i.e., the plane of the paper. 

The wave motion takes up the directions U V, and it 
can be turned into its image by a turning in the plane 
W V *'.<?., by turning out of the paper, as if the paper 

A Picture of Our Universe. 199 

were folded over about the dotted line. Then finally 
the twisting motion takes up the directions U V W, and 
can be turned into its image by being turned in the plane 
V X. That is, if each point is turned half-way round in 
this plane it becomes the corresponding point in the 
image twist. Thus on the supposition of the preceding 
pages, if a positively electrified particle could be turned 
in 4 space, it would become a negatively electrified 


IT remains now to examine if the supposition that the 
particles of a wire are twisting in strings fits in with 
observed facts of electricity. 

And firstly, if the particles are twisting in this manner, 
it is only reasonable to suppose that they would take up 
a little more room than they did when not subject to 
this movement that is, the wire would become a little 
thicker. But its volume remaining the same, if it becomes 
thicker it must compensate for this thickening by be- 
coming shorter. And it is found that a wire through 
which an electric current is sent tends to become shorter 
when the current comes into it. 

Again, suppose a wire through which a current has 
been sent suddenly isolated. It has a twist in it, and 
will keep this twist. But if it is connected up with any 
other wire forming a complete circuit through which it 
can untwist itself, it will probably do so, and in un- 
twisting would very likely overshoot the mark and 
become twisted in the opposite direction. Thus it would 
make a series of twists, each less than the last before 
becoming quiescent. And it is observed that a wire if 
so isolated does produce a rapidly alternating series of 

2OO A Picture of Our Universe. 

very minute currents before it comes to rest ; just as ir 
it were untwisting itself and overshot the mark each way 
many times before the electrical state has altogether 

The question now comes before us, How is it that a 
wire gets twisted ? Through what agency is a current of 
electricity urged through a wire, or a twist put into it ? 

This is often done by pneans of an electrical battery. 
We will take a simple instance. 

Suppose a dish f c sulphuric acid, and a bit of carbon 
and a piece of Wipe put into it. Then the carbon and 
the zinc aroj^onnected outside the liquid by a wire. 
Along this wire electricity will pass. Now the twist put 
into the wire must come from somewhere. And it is 
found that the sulphuric acid, which is a very lively com- 
pound, and contains a great deal of energy, becomes 
quieted down, and is quite different after the battery has 
finished working. On examination afterwards it is found 
to consist of sulphate of zinc. 

Sulphuric acid can be looked upon as consisting of two 
bodies hydrogen and a sulphur and oxygen compound. 
This sulphur and oxygen compound is called SO 4 . Now 
the SO 4 comes to the zinc, and with zinc forms quite a 
dead compound, with little energy in it, called zinc 
sulphate, or Zn SO 4 . The hydrogen, on the other hand, 
comes off at the carbon in an energetic state. 

Hence evidently the SO 4 has given up its energy, the 
hydrogen has not. So the twist in the wire probably 
comes from the SO 4 ; and thus the twist is started 
at the zinc end, and runs round the wire from zinc to 

At the same time we may suppose that an image 
twist, starting also from the zinc, runs through the fluid 
of the battery and then along the wire, till meeting the 
twist the two mutually unwind each other. 

A Picture of Our Universe. 201 

Thus the battery will be as if one had a loop of thread, 
and at one point twisted it between one's finger and 
thumb. Twist and image twist, starting from this point, 
unwind each other on the opposite part of the loop. 
And if the loop is not joined, but the threads are held, 
each will become twisted with increasing tension till they 
can twist no longer. The objects which hold the ends 
of the thread, and prevent them twisting, represent 

It is found that when a strong current of electricity 
passes through some water which has had a little sul- 
phuric acid added to it, two effects take place. 

In the first place some of the current passes through 
as through a wire. In the next place a part of the 
current is used up in producing an effect on the water. 
It splits the water up into two parts, each of them con- 
taining very much more energy than the water. One 
part is called hydrogen, and comes off at the wire which 
comes from the zinc, which we will call the zinc wire. 
The other part of the water comes off at the wire coming 
from the carbon, or at the carbon wire, and is called 

Let us now suppose that the twist of the zinc wire 
calls up in the molecule of water next to it an image 
twist. If it could pass on its twist at once, the water 
would form an ordinary conductor ; but the water is not 
a conductor. Hence we suppose the same relation to 
hold good between the end of the zinc wire and the 
water molecules as between the zinc wire and any other 
body to which the twist cannot be communicated. 

Now in the part of the molecule nearest the zinc wire an 
image twist is called up. And hence the molecule, being 
unable to twist as a whole, in the end of it away from 
the zinc wire a twist is produced. Thus the water 
molecule is strained into image twist and twist. Now 

202 A Picture of Our Universe. 

let us suppose that by a powerful current it is wrenched 
in two. It is separated into a part having an image 
twist " hydrogen," which comes off at the zinc wire, and 
into a part with the twist " oxygen." 

But this part with the twist calls up an image twist 
in the molecule next to it, wrenches it in two. Thus 
the oxygen of the first molecule separates up the next 
molecule into hydrogen and oxygen. The oxygen has 
a twist, the hydrogen an image twist. These twists run 
each other out, and leave an oxygen part free. 

This oxygen part does the same to the next molecule, 
and so this action is transmitted through the whole body 
of the water till the carbon wire is reached when, the 
oxygen part finding no other molecule to wrench asunder, 
is left isolated, and comes off in the form of gas. 

Thus we see that oxygen and hydrogen would be 
bodies having in them twist and image twist that is, 
that they would have an active rotation each of them ; 
but the rotation would be different in the two cases, and 
such that if put together they would run each other out : 
the light and heat produced by the union of the two 
being probably the exhibition of the effects of this 
running out. 

If we adopt the supposition, which seems most in 
accordance with facts, that there are in water two dif- 
ferent elements occurring in distinct particles, the one 
called oxygen, the other hydrogen ; and if, moreover, we 
suppose that these particles are perpetually changing 
places, and that each oxygen particle is sometimes 
linked with this hydrogen particle, sometimes with that, 
then it is obvious that the oxygen and the hydrogen in 
the water are in such a state that, if collected together 
separately, they would form liquid oxygen and liquid 
hydrogen ; and the effect of the electric twist is to give 
them those active image rotations, or strains, which 

A Picture of Our Universe. 203 

make them take the gaseous form, and assume that 
peculiar relation to each other which exhibits itself so 
strikingly in combustion. 

With regard to magnetism, the same phenomenon of a 
particular state or disturbance of matter and its image 
state or disturbance is very strikingly obvious. 

For take the case of a magnet. By the influence of 
an electric current passing round it, it can be turned into 
a magnet with opposite poles. That is to say, the small 
particles of the iron have been so shifted that, whatever 
their disposition was in the first case, they have now the 
reverse disposition. If we suppose the small particles to 
be magnets like the whole magnet, and all to have their 
north poles pointing in one direction, then after the 
action of the current they have their north poles pointing 
in the opposite direction. But they have not turned in 
space, for, if they were to turn, each must turn about 
some axis. But if there was some axis then, with regard 
to this axis, the magnetic influence would have a definite 
relation ; the turning of the particles \vould take place 
in a certain plane, and there would be a certain plane in 
the magnet which would have special properties. 

But a magnet is perfectly symmetrical in all its pro- 
perties round its axis. The magnet which has had its 
poles reversed is, as an arrangement, the image of itself 
in its first condition. In the solid mass of iron which 
forms the magnet, by the action of electricity, a particular 
arrangement and its real image are alternately pro- 

There are some very important electrical phenomena 
which have been left out of consideration altogether 
namely, the repulsions and attractions exercised by 
electrified bodies. 

Adopting the conceptions here laid down with regard 
to electricity that the two kinds are in the relation of 

204 A Picture of Our Universe. 

twist and image twist we find that certain conclusions 
force themselves upon us. 

A positively electrified body attracts a negatively 
electrified body. 

A positively electrified body repels a positively elec- 
trified body. 

Or, as it is put in a shorter form, one kind of electricity 
attracts the opposite kind, and repels the same kind. 

Now, if our theory is true, a twist ought to attract its 
image twist, and repel a twist like itself. 

And as far as can be observed it is always a fact 
that a movement of any kind taking place in a medium 
does attract its image movement, and repel a movement 
like itself. 

Some very instructive experiments have been made 
with bodies suspended in water, and caused to pulsate 
or twist. It would be found, on referring to the details 
of these experiments, that if two spheres are pulsating 
or throbbing, so that the movements of the one are at 
any instant what the movements of the other would 
seem like, if looked at in a mirror, then these two spheres 
will attract each other. If the one is a real copy of 
the other, then they repel each other. And this law 
holds good not only for throbbing movements, but also 
for twisting movements. 

If now we supposed that what held good for move- 
ments held good for tensions of the same nature as the 
movements, these results would be in exact accordance 
with our suppositions. If a twisting movement attracts 
its image twisting movement, will a twist attract its 
image twist by means of its effect on the medium in 
which it is, and on which it exerts tension ? This point 
must be left undecided. 


{HE words which I have chosen as the title 
of this paper are the expression for a process 
which has been asserted to be one that occurs 
alike in our mental and in our moral life. It 
has so happened that in certain of my own inquiries 
I have applied this process ; and the details may be of 
interest. But I must warn the reader not to expect any 
wide views on life, or far-reaching thoughts, or any of 
the warmth of human affairs. What I think about is 
Space ; and it is the application of the principle of cast- 
ing out the self in attaining a knowledge of Space about 
which I have something to say. 

And, firstly, as a bit of absolute human experience 
is never without value, but that which we make up is 
often so, I may as well cast the fear of ridicule aside 
and enable the reader to take in, in a few lines, the 
exact commencement of my inquiry. 

The beginning of it was this. I gradually came to 
find that I had no knowledge worth calling by that 
name, and that I had never thoroughly understood any- 
thing which I had heard. I will not go into the matter 
further ; simply this was what I found, and at a time 
when I had finished the years set apart for acquiring 
knowledge, and was far removed from contact with 
learned men. I could not take up my education again, 


206 Casting out the Self. 

but although I regretted my lost opportunities I de- 
termined to know something. With this view I tried 
to acquire knowledge in various ways, but in all of 
them knowledge was too impalpable for me to get hold 
of it. And I would earnestly urge all students to make 
haste in acquiring real knowledge while they are in the 
way with those that can impart it ; and not rush on too 
quickly, thinking that they can get knowledge after- 
wards. For out in the world knowledge is hard to find. 

At length I came to find that the only thing I could 
know was of this kind. If, for instance, there were 
several people in a room, I could not know them them- 
selves, for they were too infinitely complicated for my 
mind to grasp ; but I could know if they were at right 
or left hand of one another, close together, or far apart. 
And the same of, to take another instance, botanical 
specimens in a book. I could not grasp the specimens 
each was too infinitely complicated, and each part too- 
infinitely complex but I could tell which specimen was 
next which. 

Accordingly, being desirous to learn something 
thoroughly, and since, in the arrangement of any dif- 
ferent objects, there was such a lot of ignorance intro- 
duced by the objects being different each bringing in 
its own ignorance and feeling of bewilderment I deter- 
mined to learn an arrangement of a number of objects 
as much alike as possible. 

Accordingly I took a number of cubes, which were as 
simple objects as I could get, arranged them in a large 
block, and proceeded to learn how they were placed with 
regard to each other. In order to learn them I gave each 
of them a name. The name meant the particular cube 
in the particular position. 

Thus, taking any three names, I could say, about the 
three cubes denoted, ho\v they were placed with regard 

Casting out the Self. 207 

to one another : one, say, would be straight above the 
first with four intervening, the third would touch the 
second on the right hand, or some similar arrangement. 

Now in this way I got what I conceived to be know- 
ledge. It was of no use or beauty apparently, but I had 
no reason to use it or to show it. 

It is about this bit of knowledge that I want to speak 
now a block of cubes, and the cubes are known each 
one where it is. 

Sometimes I have been tempted to call this absolute 
knowledge, but have been reminded that I did not know 
the cube itself. Against this I have argued. But in argu- 
ment we say many things which we do not understand, 
and my conclusion is, on the whole, that the objection 
is well founded. Still, if not knowledge absolute, the 
knowledge of this block approaches more nearly to 
knowledge absolute than any other with which I am 
acquainted, because each cube is the same as its neigh- . 
bour, and instead of an arrangement of all sorts of 
diverse ignorances we have only one kind of ignorance 
that of the cube. Each of the cubes was an inch each 
way, and I learnt a cubic yard of them. That is to say, 
when the name of any cube was said, I could tell at 
once those which it lay next to ; and if a set of names 
were said, I could tell at once what shape composed of 
cubes was denoted. There were 216 primary names, 
and these, taken in pairs, were enough to name the cubic 

For the practical purpose of this paper, however, it 
will suffice if the reader will imagine a block of twenty- 
seven cubes, forming a larger cube, each cube being 
denoted by a name (see Diagram I. below). Then it is 
evident that two names mean a certain arrangement 
consisting of two cubes in definite places with regard to 
one another three names denote three cubes, and so on. 


Casting out the Self. 

And I would ask the reader not to mind taking a little 
trouble at this point, and to look at the diagram for a 
little while. If there is anything about which we can 
form perfectly clear ideas, it is a little heap of cubes. 
And if the reader will simply look at them for a little 
space of time, he will realize clearly every word of what 
I have to say ; for I am going to talk about nothing else 
than this little block of cubes. 

Thus, looking at the cube with the figure I upon it, 
this numeral will serve for the name of the cube, and 

similarly the number 
written on every cube 
will serve for its name. 
So if I say cubes I 
and 2, 1 mean the two 
which lie next to each 
other, as shown in the 
diagram ; and the 
n u m b e rs 

i> 4, 7> 

above each other. If I say cubes I and 10, I mean 
the first cube and one behind it hidden by it in the 

Now this is the bit of knowledge on which I propose 
to demonstrate the process of casting out the self. It is 
not a high form of knowledge, but it is a bit of know- 
ledge with as little ignorance in it as we can have ; and 
just as it is permitted a worm or reptile to live and 
breathe, so on this rudimentary form of knowledge we 
may be able to demonstrate the functions of the mind. 
And first of all, when I had learnt the cubes, I 

x^ / S7 / S<9 



/ & / & 
















Diagram I, a block consisting of 27 cubes. 

Diagram II. 

Casting out the Self. 209 

found that I invariably associated some with the idea 
of being above others. When two names were said, I 
had the idea of a direction of up and down. But with 
regard to the cubes themselves, there was no absolute 
direction of up or down. I only conceive of an up 
and down in virtue of being on the earth's surface, and 
because of the frequent experience of weight. Now this 
condition affecting myself I found was present in my 
knowledge of the cubes. When certain of the names 
were said, I conceived of a figure having an upper part 
and a lower part. Now, considered as a set of cubes 
related to one another and not to me, the block had 
nothing to do with up and down. As long ago as 
Ptolemy, men have known that there is no such thing 
as an absolute up and an absolute down. And yet I 
found that in my knowledge of the set of cubes there 
was firmly embedded this absolute up and this absolute 
down. Here, then, was an element arising from the par- 
ticular conditions under which I was placed, and the 
next step after recognizing it was to cast it out. This 
was easily done. The block had to be turned upside 
down and learnt over again with the cubes all in their 
new positions. It was, I found, quite necessary to learn 
them all over again, for, if not, I found that I simply went 
over them mentally the way first learnt, and then about 
any particular one made the alteration required, by a 
rule. Unless they were learnt all over again the new 
knowledge of them was a mere external and simulated 
affair, and the up and down would be cast out in name, 
not in reality. It would be a curious kind of knowing, 
indeed, if one had to reflect what one knew and then, 
to get the facts, say the opposite. 

It may seem as if, when the cubes were known in an 
upright position, they would be easily imagined in an 
inverted position. But practice shows that this is very 

2io - Casting out [he Self. 

far from being the case. It requires considerable mental 
effort to determine the alterations in position, and to 
get an immediate knowledge requires a considerable 

It may seem as if it were a dubious way of getting 
rid of gravity, or up and down, just to reverse the action 
of it. 

But this way is the only way, for we, I have found, 
cannot conceive it away ; we have to conceive it acting 
every way, then, affecting each view impartially, it affects 
none more than another, and is practically eliminated. 

The cube had not only to be turned upside down, but 
also laid on each of its sides and then learnt. There 
were a considerable number of positions, twenty-four in 
number, which had to be brought close to the mind, so 
that the lie of each cube, relative to its neighbours and 
the whole block, was a matter of immediate apprehen- 
sion in each of the positions. 

If a single cube be taken and moved about, it will be 
found that there are twenty-four positions in which it 
can be put by turning it, keeping one point fixed, and 
letting each turning be a twist of a right angle. The 
whole block had to be turned into each of these posi- 
tions and learnt in each. 

Thus the block of cubes seemed to be thoroughly 

At any rate, up and down was cast out. And we can 
now attach a definite meaning to the expression "casting 
out the self." One's own particular relation to any object, 
or group of objects, presents itself to us as qualities 
affecting those objects influencing our feeling with 
regard to them, and making us perceive something in 
them which is not really there. 

Thus up and down is not really in the set of cubes. 

Now these qualities or apparent facts of the objects 

Casting out the Self. 2 1 1 

can be got rid of one at a time. To cast out the self is 
to get rid of them altogether. 

As soon as I had got rid of Up and Down out of the 
set of cubes I was struck by a curious fact. 

If in building up the block of cubes one goes to the 
left instead of to the right, keeping all other directions 
the same, a new cube is built up having a curious rela- 
tion to the old cube. It is like the looking-glass image 
of the old cube. Every cube in the new block corre- 
sponds to every cube in the old block, but in the new 
figure it is as much to the left as before it was to the 
right. And any set of names in the block so put up 
gives a shape which is like the shape denoted by the 
same set of names in the old block, but which cannot be 
made to coincide with it, however turned about. It 
is the looking-glass image of the old shape. The one 
block was just like the other block, except that right 
was changed into left. Now, was it necessary to cast out 
right and left as had been done with up and down ? or 
was right and left, as giving distinctions in the block and 
in shapes formed of cubes, to remain ? It seemed as if 
right and left belonged more to me than to the set of 
cubes. And yet the right-handed set of cubes could not 
be made by moving about to coincide with the left- 
handed set of cubes. And this power of coincidence 
was the test which had convinced me of the self nature 
of " Up and Down." 

Let Diagram I. represent a small block of cubes. It is 
itself in the form of a cube, and it contains 27 cubes. 
For purposes of reference we will give a number to each 
cube, and the number will denote the cube where it is. 

In the front slice are cubes numbered from I up to 9, 
in the second slice are cubes numbered from 10 to 18, 
and so on. Thus behind I is the cube 10. This cube 
and the cube n are hidden, but the cube 12 is shown in 
the perspective. 

212 Casting out the Self. 

Now in this block of cubes there is a part which is 
known and a part which is unknown. The part which 
is known is how they come or the arrangement of them. 
The part that is unknown is the cube itself, repetitions 
of which in different positions forms the block. 

The cube itself is unknown, because, being a piece of 
matter, it possesses endless qualities, each of which grows 
more incomprehensible the more we study it. It is also 
unknown in having in it a multitude of positions which 
are not known. The cube itself is, amongst other things, 
a vastly complicated arrangement of particles. Hence, 
putting all togetJier, we are justified in calling the cube 
the unknown part ; the arrangement, the known part. 

The single cube thus is unknown in two ways. It is 
unknown in respect to the qualities of hardness, density, 
chemical composition, &c. It is also unknown as a 
shape. If it really consisted of a certain number of 
parts, each of which was clear and comprehensible in 
itself, then we should know it if we grasped in our minds 
the relationship of all these parts. But there are no 
definite parts of which a cube can be said to be made 
up. We can suppose it divided into a number of exactly 
similar parts, and suppose that all are like one of these 
parts. But this part itself remains, and the problem re- 
mains just the same about this part as about the whole 

Now there is a double perplexity: one about the nature 
of the matter, the other about the cube as to the arrange- 
ment of its parts. We will give up any question about 
the matter of which the cube is composed ; to know any- 
thing about that is out of the question. But, supposing 
it to be of some kind of matter, it presents an inex- 
haustible number of positions. It can be divided again 
and again. 

Let us look at the block again, and for the moment 

Casting out the Self. 213 

dismiss from our minds the question just raised as to the 
single cubes of which it is built up. Let us look on each 
of these cubes as a unit. Then two of the units, taken 
together, form a shape ; three or five of them would form 
a more complicated shape, and so on. 

We can also suppose the cubes away, and think 
merely of the places which they occupied. In this 
manner, by first thinking of the 27 cubes, and then 
simply by keeping the places of them in our minds, 
we get 27 positions, and in these positions we can 
suppose placed any small objects we choose. Each of 
these positions may be called a unit position, and we 
can form different arrangements of small objects by 
putting them in different ones of these positions. Now 
in all this we do not divide the cube up. We simply 
think of it as a whole we think of it as a unit. Or if 
we take the room of the cube instead of the cube, and 
think of the place it occupies, which I call a position, we 
do not divide that position up. We take it, if I may use 
the expression, as a unit position. And without asking 
any question as to tJie nature of these positions, whether 
they are complicated ideas or not, we have a kind of 
knowledge of the whole block, in that it consists of this 
collection of 27 cubes, or of this set of 27 positions. 

Thus in a rough and ready manner there is something 
which we can take. If we do not inquire about one of 
the cubes itself, we are all right ; that being granted we 
can know the block. 

But if we look into what each of these unit cubes, or 
what each of these unit positions is, we find quite an 
infinity opening before us. There is nothing definitely 
of which we can say that the whole unit cube is built 
up, and each of the positions has a perfectly endless 
number of positions in it, if we come to examine it 
closely. All that we can say is that our ignorance 

214 Casting O'.it the Self. 

about each of the unit positions is of the same kind 
as our ignorance about every other, and, taking one as 
granted, we may as well take the 27 as granted ; and 
so out of a lot of similar ignorances we get a kind of 
knowledge of the whole. And this knowledge is not 
a mere indefinite thing, but it can be worked at, im- 
proved, and made perfect after its kind. For suppose 
we limit ourselves to the 27 positions numbered in 
Diagram I. Two of these positions form one shape, 
three of them will form another shape, and so on. And 
in going over each of these arrangements we gradually 
get to kno\v the whole set of them which form the 

Having given up for the time any question as to the 
possible subdivisions of the cube, and looking on each 
cube as a unit position, we have 27 positions. These 
positions can be taken in different selections, and each 
selection is a shape. To know the block or set of 
positions means to form a clear idea of every shape, con- 
sisting of selections of positions, which can be formed out 
of the 27. 

But each of the cubes, 27 of which form the whole 
block, can be divided up. Each of these cubes contains 
a great many positions. There must, for instance, be 
positions in each cube for every one of its molecules. 

Thus it is evident that the cube supplies an inex- 
haustible number of positions to be learnt. I call the 
cube unknown in the sense that there are a great number 
of positions in it which are not clearly realized by the 

By a very simple device it is possible to penetrate a 
little into the unknown part. The whole set of cubes 
forms a cube. Let us consider the small cube to be a 
model of the whole cube. Let us consider it as consist- 
ing of 27 parts, each related to the other as the 27 first 

Casting out the Self. 215 

cubes were related amongst themselves. Thus the un- 
known part, the material cube, which is used to build up 
the whole, becomes reduced in size. Fig. II. represents 
such a cube. 

This is the theory. The practical work consisted in 
learning the names denoting these smaller cubes in con- 
nection with their positions, so that, the names being said, 
the small cubes meant were present to the mind, and a 
set of names being said, the shape, consisting of a set of 
cubes in definite relations to each other, came vividly 
before one. A complete knowledge of the block of cubes 
would be a complete appreciation of all the possible 
shapes which selections of the cubes would form, and 
this I strove to attain. Here at length I found real 
knowledge, and after a time I was able to reduce the 
size of the unknown still further, and to obtain a solid 
mass of knowledge fairly well worked all through. 

And now it all seemed satisfactory enough. There 
was real knowledge in knowledge of the arrangement ; 
and the material cube, which must be assumed, could be 
made smaller and smaller, it could be turned into know- 
ledge, thus affording a prospect of obtaining endless 
knowledge. Thus I found the real home of my mind, the 
only knowledge I had ever had, and I hoped always to 
continue to add to it, and always to reduce the unknown 
in size. 

Presently, too, the forms of the outward world began 
to fall in with this knowledge ; and as the mass of known 
cubes became larger in number, a group of them would 
fairly well represent a wall, a door, a house, a simple 
natural object such as a stone or a fruit. 

Yet amidst all this delight I became conscious, dimly 
enough, of a self-element in the knowledge of blocks. 

If, putting up the block of cubes, we go to the left 
instead of the right, but in all other respects build up in 


Casting out the Self. 

the same way, we obtain a block which has a curious 

relation to the first block. 

The ordinary block is shown over again in Diagram 

III. Diagram IV. is the new block. The new block is 

like a looking-glass image of the old block. It is just 

the same, but 
that left and 
right is re- 

Also, if we 
take selec- 
t i o ns of 
blocks we get 
figures which 
are just re- 
versed. Thus 

^ ^ * / & 











6 , 





Diagram III. 
is a block. 

i, 4, 7, 8, in 
' Block III., 
means a figure 
turned to the right; 
in Block IV. a figure 
turned to the left. 
Again, consider the two figures 
formed by selecting the cubes 
i, 4, 7, 8, 17, from Diagrams III. 
and IV. respectively. We get 
two figures which are just like 
Diagram v O ne another as arrangements, but 

\ T hich we cannot turn into one another by twisting. 

Considered as arrangements in themselves, these 
figures and these blocks seem to be identical, for the 
relationships of cube to cube which are present in 
the one are all present in the other. But considered 
as shapes they are not identical. For they will not 

Casting out the Self. 


The whole matter becomes much more clear if we 
consider the relationship between the individual cube 
used and the block which it forms. 

There are two starting-points, either of which we can 
adopt. We can start with the real material cube, or we 
can start with the act of arranging. When I speak of 
the real material cube 
I do not want to call 
attention to 
the kind 
which it 
composed, or 
to the nature 
of matter, but 




to the fact 

that it is to 

be a real cube 

such as can 

be made, and 

which, if one 

edge or corner be 

marked, will retain 

that mark just where 

is not a product of 

but an object, with 

objects in general. 

the real material 

the cube shown in Dia ff ram VI - 

is the model on a small scale of the 












Diagram IV. 
is its image block. 

it is a cube which 
the imagination, 
the properties of 

Let us start with 
cube. Let us take 
Diagram V., which 

Block III. The 

numbers in it show the small cubes of which we suppose 
it to be built up after the pattern of Block III. The 
numbers also serve to show the distinction of positions 
that is, \ve can refer to the right-hand corner or edge, &c., 
by saying the numbers of the small cube which lies there. 


Casting out tJie Self. 

Now, using the cube of Diagram V. to build up the 
block in Diagram III. we get a perfectly orderly result, 
as shown in Diagram VII., and we can go to bigger and 
bigger blocks, or down to smaller and smaller ones with- 
out any hitch. But if we use the cube of Diagram V. 
to build up the block of Diagram IV., there is a disad- 
justment which can be discerned in Diagram VIII. Thus, 
when V. is used to build up III., the small cubes in V, 
1,4, 7, lie in same edge as the cubes i, 4, 7, in the big 
Cube III. But when V. is used to build up IV., the small 




























1 2 3 

Diagram VII. Block III. built up with Diagram VIII. Block IV. built up 
Cube V. with Cube V. a disadjustment. 

cubes 3, 6, 9, lie on the edge which is occupied by the 
cubes i, 4, 7, in big Cube IV. 

Thus, if the same material cube is used, there is a 
disadjustment, and the figure IV. cannot be considered 
the same as the figure III. even as an arrangement, for 
the same parts of the cubes do not lie in an analogous 
manner. A certain corner of Cube V. is marked with 
the figure 7 ; this corner would be on the outside in Block 
III., but in building up Block IV. it would lie on the 

It is somewhat difficult to express this fact, but if the 
real cubes are looked at it becomes perfectly obvious. 

Casting out the Self, 219 

Imagine the whole Block III. to be built up of a num- 
ber of cubes, every one of which is alike. If the sides of 
these cubes be distinguished by any markings if, for 
instance, the left-hand side is blue and the other sides 
are each of some special colour, then on building up 
the whole block the left-hand side of the whole block 
will be blue. 

If, now, the same cubes be taken, and the attempt be 
made to build up *he looking-glass image of the block 
with them, it will be found that there will be a disadjust- 
ment. If the blue sides are made to go to the right, as 
they must, to form an image block, then some other sides 
will be in different places to what they should be in order 
to produce an image of the original block. Although 
considered as an arrangement of cubes the new block 
will be an image of the original block, still, looking at 
the individual cubes of which it is composed, it will be 
seen that the new block is not an exact image of the old 

If, however, we take the other starting-point, and, not 
assuming any fixed fundamental cube, look only at the 
act of arrangement, the two Blocks, III. and IV., are 
found to be identical in every internal relationship. 

For, taking the act of arrangement as the basis, if, 
when we have built up the Block IV., we look upon each 
of the cubes as an arrangement of the same kind as the 
whole, then the cube i in Diag. IV. is represented in 
Diag. VI. And it is evident that if Diag. IV. is built up 
out of cubes like Diag. VI., the small cubes, 1,4, 7, lie 
in the same edge as the cubes I, 4, 7, in Diag. IV. Thus 
it will be found for every relationship in Diag. III. there 
is an exactly similar relationship in Diag. IV. 

In this case if, for the sake of material illustration, we 
use marked cubes, it seems that we must not suppose 
each particular cube to have a fixed marking of its own, 

22O Casting out the Self. 

but that we must suppose the markings to spring up on 
the sides of the cubes in accordance with the places into 
which they are put. 

There is another manner of regarding the matter 
which may help to bring out the point at issue. 

If we suppose that we are putting up the cubes in one 
room while another person is putting up cubes in an 
adjoining room ; if we can tell him what we are doing, 
using the words right and left, he will be able to put up 
a block exactly like ours. But if we do not allow our- 
selves to use the words right and left, but speak to the 
other person as if he were simply an intelligence without 
having the same kind of bodily organization as ourselves, 
we should find that, supposing he could put up the block 
of cubes, it would be a mere matter of chance whether he 
had put up the block as we had put it, or whether he 
had put it up in an image way. And the same with 
regard to any shape. We could tell him that the cubes 
should be put together, and we could tell him the 
relationship which they should have with regard to one 
another ; but the figure he put up would just as likely be 
an image of our shape as not. 

And we could go on for ever building more and more 
complicated shapes and telling him to do the same, 
and no hitch or difficulty would come. But at the end 
all his shapes might be ours just reversed, as if seen in a 

And if, having put up the block, we coloured the sides 
of the cube we used as the fundamental cube, and told 
him how we had coloured it : if he coloured his and 
brought it to us, and we compared them, his would just 
as likely be the image of our cube, and not able to be 
turned into it. So that although, as arrangements, the 
structures we had put up were alike, still neither of us 
could use the other's fundamental cube ; and if we ex- 

Casting out the Self. 221 

changed the fundamental cubes there would be an in- 
consistency in each of our arrangements. 

Now, are these blocks of cubes really the same ? Are 
III. and IV. really the same in themselves, as all relation- 
ships in the one are to be found in the other ? If so, the 
feeling on my part that they are different, and the in- 
conceivability of their coinciding, must be due to some 
self-element which is mixed up with my apprehension 
of the cube. 

The Block IV. is like the Block III. in its known part 
in its arrangement. It is unlike Block III. in its un- 
known part the cube which must ultimately be supposed 
as the fundamental cube, by using which over and over 
again the whole is built up. 

Now, the properties of the unknown part the little 
cube of matter which of some size or another, we must 
assume, are so mysterious that one does not feel any 
argument very safe which rests on it. 

Moreover, there is a very obvious consideration which 
reduces the importance of the part played by the 
material cube very considerably. 

It is possible to consider the Cube V., which is used to 
build up III., as the total of 27 cubes. 

But each of these cubes the small cubes in Diag. V. 
can be considered to be made up of 27 still smaller cubes. 

By going on in this way we can get our fundamental 
cube very small indeed. The difference between the 
Cubes III. and IV., in respect to this fundamental cube, 
will still remain. But omitting this difference they will 
be, considered as arrangements, identical. 

To state the matter over again. We start with a real 
cube, one inch each way, and build up the block in 
Diagram III. with it. If we try to build up the block 
in Diagram IV. with this same inch cube, we find that 
there is a disadjustment. 

223 Casting out the Self. 

But we are not obliged to have our fundamental cube 
Due inch in size. We can take it as small as we like, 
and build up the block, using a greater number of such 
cubes. We can take it the twenty-seventh of the twenty- 
seventh of an inch cube ; or, in fact, as small as ever we 
like. And if we take a very small cube as the funda- 
mental one with which we build up the Block III., then, 
using this same fundamental cube to build up Block IV., 
we should find a disadjustment, although this disad- 
justment would only come in when we come down to 
the very minute cube, and studied its relationship to 
the whole Block IV. 

Thus, apparently, the Block IV. could never be built 
up consistently, using as its fundamental cube the fun- 
damental cube out of Block III. But in saying this we 
have really made an assumption. 

It is obvious that Cubes V. and VI., just like Cubes 
III. and IV., considered as shapes made up of matter, 
arc very different, and could not be shifted one on to 
the other. 

But all our laws and feelings about movements and 
possibilities are founded on the observation of objects 
having a certain degree of magnitude. 

But the fundamental cube, which we must assume, 
may be supposed to be of a degree of magnitude less 
than any known degree. 

In cubes of a certain size V. and VI. are different, and 
cannot be made to coincide. 

But we are absolutely unable to say anything about 
cubes beyond a certain degree of smallness. With cubes 
of a certain degree of minuteness, V. and VI. might be 
able to be made coincide. 

Thus, for instance, we feel as if we could divide a 
piece of matter on and on for ever. But chemists tell 
us that, after a certain number of divisions, the next 

Casting out the Self. 223 

division would split it up into two different kinds of 
matter. Since all our reasoning is founded on the 
behaviour of objects of known size, we can tell nothing 
at all by inference about the behaviour of very small 

It is obvious that, from our customary experience, we 
can assert absolutely nothing at all about the extremely 
minute or the extremely large. All reasoning which is 
founded on the likeness between the extremely small 
and the ordinary objects of our observation is absolutely 
valueless as telling us any truth. 

Of course, by saying this we have not got rid of the 
argument for the difference of III. and IV. But we 
have put the thing from the observation of which that 
argument is drawn out of the region of known things. 
We have put it into the hazy land of the extremely 
minute. Its argument is good, but it depends on its 
being of a certain size. We suppose it less than that 
size, and we can consider the subject without regard 
to its argument. 

The question then before me was, Is " Right and Left " 
to be cast out ? And connected with this was the 
consideration of whether it was possible for extremely 
minute cubes to be " pulled through," that is, to be treated 
somehow which would turn one like V. into one like VI. 

Now, if " right and left " was a self-element, it could 
be cast out ; if it was a permanent distinction in the 
cubes themselves, it could not be cast out. The thing to 
do was evidently to try. The method was to learn the 
cubes over again, in a set of new positions. For every 
one of the ways in which they were learnt before, there 
was an inverted or pulled through way to be learnt. 

While I was engaged in this attempt another inquiry 
suddenly coincided with this, and explained it all. 

Much has been said about the fourth dimension of 

224 Casting out the Self. 

space and the inconceivability of it to us. Now, if there 
are beings who live in a four-dimensional world, they 
must feel as habituated to it as we do to ours, and the 
conceptions which seem so impossible to us must be 
e very-day matters to them. It would be impossible for 
us to try to enter at once into the serious thoughts of 
these denizens of higher space. But amongst them 
there would probably be some with whose occupations 
we might become familiar, and with whose ideas we 
might gain some acquaintance. Amongst these beings 
there must be children, and just as children on the 
earth gain their familiarity with space by means of 
bricks and blocks and toys, so these higher children must 
have their own simple objects wherewith they grow into 
familiarity with their complex world. 

Now it is easy to make a set of simple objects such 
as these higher children would use. And it seemed a 
practical thing to do with regard to the conceivability 
or inconceivability of the fourth dimension to give the 
matter a fair trial, by going through those processes 
and those experiences which must be gone through by 
the beings in higher space to gain their acquaintance 
with it. 

When I say that it is easy to make a set of objects, 
such as the higher children use, I do not mean to say 
that they can be made completely in every part at once. 
But we can make the ends and sides of them, and \ve 
can look at the ends and Slides of them as they appear 
to us in space, and we carf make up exactly what sides 
come into space when the simple objects are twisted and 

Just as a being living on a plane could tell about all the 
faces and edges of a cube or other simple solid figure by 
looking at what he could see when the cube was laid on 
his plane, and when it was twisted and laid down again ; 

Casting out the Self. 225 

so we can tell all about the sides, faces, and edges of a 
higher solid. 

And the project seems less uninviting if we reflect on 
how complicated a matter the formation of our own 
conceptions of a solid are. What a lot of faces and 
edges a cube has ! And, moreover, it must be remem- 
bered that we never touch or see a solid ; we only see the 
surface and touch the surface. If we cut away the 
surface that we first saw or touched, we come on 
another surface, and so on. 

Now, of course, the surfaces of a solid are given to us 
by nature in their right connection and relation. Each of 
the edges of the cube, for instance, can be noticed and 
remarked without any difficulty, and they are all on the 
same bit of space, to be looked at one at the same time 
as another. 

But the sides, faces, and edges of a higher solid cannot 
be in our space all at once. They must come separate!} 7 , 
be looked at one by one. 

Thus a being in a plane could not see the lower side 
and the front of a cube at once. He would first have to 
look at the lower side as the cube rested on his plane, 
then if the cube were turned over he would see the 
front, and the lower side would be gone. If he got the 
set of right appearances which a cube would present to 
him when, turning about in a systematic way, it came 
at intervals into his plane, and if, moreover, he fixed 
his mind on these appearances, he might at last, if it 
was in him, rise to the conception of a cube as we 
know it. 

Now, the parts by which a higher solid comes into our 
space are solids, and what we have to form is a set of 
solids coming and going in a systematic way, as the 
higher figure is moved about in a systematic way. 

This afforded a welcome exercise, for conceiving the 

226 Casting out the Self. 

solid shapes, and how they went and came, increased my 
familiarity with the set of cubes. 

Moreover, in trying to get the piece of ignorance the 
necessary real cube as small as possible, I had got the 
block which I knew to a somewhat fine state of division, 
and could, by picking out a particular set of cubes from 
the whole number, obtain a mental model of any shape I 
wanted. The whole block of cubes formed a kind of 
solid paper in which one could mentally put down any 
solid shape one wanted. And just as it is a great con- 
venience to have a piece of paper for drawing figures one 
wants to think about, so it was a great convenience to 
have this solid paper. 

The subject, however, abounds in abysses for stupidity 
to fall into, and I had to clamber out of each of them ; 
so it took me several years before I got quite on the 
right tack. Then it was easy enough : any one in a few 
weeks could learn to conceive four-dimensional figures. 
Not only is it easy, but there are abundant traces that we 
do it continually without being aware of it. I am sure 
if the loveliness of the work while one is doing it, and 
the simplicity and self-evident nature of the results when 
obtained, were generally known, it would be a favourite 

Now one of the first things that presented itself to 
my attention when I began to move the four-dimensional 
figures about was a fact which bore curious reference to 
my difficulty about the fundamental cube. If the reader 
remembers, it seemed to me as if the cube out of which 
the whole block of known cubes was built ought to be 
able to be inverted. That is to say, it seemed to me that 
there was a self-element present in my knowledge of the 
cubes. But in order to cast out that self-element the fun- 
damental cube which lay at the basis of the whole block 
would have to be able to be inverted, or pulled through. 

Casting out the Self. 227 

Now I found that when I took a four-dimensional 
figure which came into space by a cube that is, a figure 
which rested on space by a cube, or one of whose sides 
was a cube when I took a figure of that sort up in the 
fourth dimension and twisted it round and brought it 
down again, this cube would sometimes be inverted or 
pulled through although I had done nothing to it, but 
had simply twisted the whole figure round without 
disturbing the arrangement of its parts. 

Thus evidently to a higher child it would be no more 
difficult to invert or pull through a cube or a figure than 
it would be to me to twist one round. 

Hence it was obvious that right and left was really a 
self-element in my block of cubes. I being in our space 
was under a certain limitation, and that limitation made 
me feel as if a right-handed arrangement was different 
from a left-handed arrangement. 

A being who was not limited as I was would see that 
they were one and the same. Hence, in knowing the set 
of blocks it was necessary to cast out " right and left," 
and the names had to be learnt over again in new 

Thus it is evident that there are three expressions 
which may be considered in reference to a knowledge of 
a block of cubes as almost identical : " Casting out the 
self" "Seeing as a higher child" and thirdly, "Ac- 
quiring an intuitive knowledge of four-dimensional 

Thus, taking the simplest and most obvious facts the 
arrangement of a few cubes we found that there was a 
known part and an unknown part ; the known part 
corresponding to our act of putting, the unknown part 
the cube which, of some size or another, must be taken as 
given in the external world. Then there was obviously 
a self-element present in the Up and Down felt as in the 

228 Casting out the Self. 

cubes. This being removed, Right and Left had also to 
go. So, to get the knowledge of this simple set of objects 
clear of self-elements, two universe transforming thoughts 
have to be used ; and when these thoughts are thus in- 
corporated the cubes become different. 

It will be obvious to the reader that in these pages I 
have merely touched the surface of the subject. But the 
deeper matters which are contained in the knowledge of a 
block of cubes are difficult to express, and are so mixed 
up with the practical work, as far as I conceive them at 
present, that it is best to consider in some detail the 
applications to the world about us of those truths of 
which we have already got a clear apprehension from 
the block of cubes. 

Instead, then, of going on, let us conclude the present 
paper by going back, and taking a simple instance of the 
general truth that progress in the knowledge of a block 
of cubes is casting out the self. 

Let the reader turn to Diagram I. and make out the 
shape which the following numbers denote namely, I, 
4, 5. If the following numbers be said, 18,27,26, it will be 
found that they denote the same shape, but in a different 
position. Now if the block of cubes be well known, these 
two sets of names, 1,4, 5, and 18, 27, 26, ought to convey 
instantly to the mind the same idea. However quickly 
they are realized, it ought to be evident that they are the 
same shape. 

And a good deal of the practical work in learning a 
block of cubes consists in gaining this faculty of immediate 
apprehension. But when it is gained it is seen to consist 
much more of getting rid of an imperfection than in 
being any real advance. For if the two shapes are 
identical we need not ask ourselves how it is we see them 
as the same, but we have to ask ourselves what is the 
reason why we do not recognize their identity ; and 

Casting out the Self. 229 

the answer evidently is that, if we do not recognize their 
identity, it is due to the particular relationship of each 
shape to ourselves. One is down on our left hand, 
another is up on our right, and they are turned relatively 
to us different ways. Now these differences, which are 
merely relative to us, we impress upon the shapes, and 
really feel the shapes to be different. The practice con- 
sists in getting rid of the influence of these self-elements, 
so that two shapes, however complicated, being alike, 
when their names are said, we feel them to be alike with- 
out calculation or reflection. Thus the power of seeing 
likeness and analogy in this domain is merely another 
name for the power of casting out the self-elements 
from our mental presentation of any objects with which 
we come into contact. 

000 676 726